Skip to main content Accessibility help
×
Home
Stability Regions of Nonlinear Dynamical Systems
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 22
  • Export citation
  • Recommend to librarian
  • Buy the print book

Book description

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.

Reviews

This book offers a comprehensive exposition of the theory, estimation methods, and applications of stability regions and stability boundaries for nonlinear dynamical systems. … All the proofs are given in a rigorous manner and various examples are presented for illustration. The book is written concisely and will provide very useful guidance for researchers and graduate students who are interested in dynamical systems and their applications.'

Vu Hoang Linh Source: Mathematical Reviews

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents


Page 1 of 2



Page 1 of 2


[2]Abraham, R., Robbin, J., Transversal Mappings and Flows, Benjamin, New York, 1967
[3]Ailon, A., Segev, R., Arogeti, S., “A simple velocity-free controller for attitude regulation of a spacecraft with delayed feedback”, IEEE Transactions on Automatic Control, v.49, n.1, pp.125130, Jan 2004
[4]Alberto, L. F. C., Transient Stability Analysis: Studies of the BCU method; Damping Estimation Approach for Absolute Stability in SMIB Systems (In Portuguese), Escola de Eng. de São Carlos – Universidade de São Paulo, 1997
[5]Alberto, L. F. C., Calliero, T. R., Martins, A., Bretas, N. G., “An invariance principle for nonlinear discrete autonomous dynamical systems”, IEEE Transactions on Automatic Control, v.52, n.4, pp.692697, Apr 2007
[6]Alberto, L. F. C., Chiang, H. D., “Controlling unstable equilibrium point theory for stability assessment of two-time scale power system models”, IEEE Power and Energy Society General Meeting, Pittsburgh, PA, pp.19, 2008
[7]Alberto, L. F. C., Chiang, H. D., “Uniform approach for stability analysis of fast subsystem of two-time-scale nonlinear systems”, International Journal of Bifurcation and Chaos, v.17, n.11, pp.41954203, 2007
[8]Alberto, L. F. C., Chiang, H. D., “Characterization of stability region for general autonomous nonlinear dynamical systems”, IEEE Transactions on Automatic Control, v.57, pp.15641569, 2012
[9]Amaral, F. M., Alberto, L. F. C., “Stability region bifurcations of nonlinear autonomous dynamical systems: type-zero saddle-node bifurcations”, International Journal of Robust and Nonlinear Control, v.21, n.6, pp.591612, 2011
[10]Amaral, F. M., Alberto, L. F. C., “Type-zero saddle-node bifurcations and stability region estimation of nonlinear autonomous dynamical systems”, International Journal of Bifurcation and Chaos in Applied Science and Engineering, v.22, n.1, p.1250020 (16 pages), 2012
[11]Amaral, F. M., Alberto, L. F. C., “Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points”, TEMA Tendências em Matemática Aplicada e Computacional, v.13, pp.143154, 2012
[12]Amaral, F. M., Alberto, L. F. C., Bretas, N. G., “Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of a type-zero saddle-node equilibrium point”, TEMA Tendências em Matemática Aplicada e Computacional, v.11, pp.111120, 2010
[13]Amato, F., Cosentino, C., Merola, A., “On the region of attraction of nonlinear quadratic systems”, Automatica, v.43, pp.21192123, 2007
[14]Anderson, B., Keller, J., “Discretization techniques in control systems”, Control and Dynamic Systems, v.66, pp.47112, 1994
[15]Arnold, V., Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, 1977
[16]Arrow, K. L., Hahn, F. H., General Competitive Analysis, Holden Day, San Francisco, CA, 1971
[17]Artstein, Z., “Stability in the presence of singular perturbation”, Nonlinear Analysis, v.34, pp.817827, 1998
[18]Aylett, P. D., “The energy integral-criterion of transient stability limits of power systems”, Proceedings of the IEEE, v.105, n.8, pp.527536, Sept 1958
[19]Baer, S. M., Li, B. T., Smith, H. L., “Multiple limit cycles in the standard model of three species competition for three essential resources”, Journal of Mathematical Biology, v.52, n.6, pp.745760, Jun 2006
[20]Baillieul, J., Byrnes, C. I., “Geometric critical point analysis of lossless power system models”, IEEE Transactions on Circuits and Systems, v.29, pp.724737, 1982
[21]Baker, J., “An algorithm for the location of transition states”, Journal of Computational Chemistry, v.7, n.4, pp.385395, 1986
[22]Balu, N., Bertram, T., Bose, A., Brandwajn, V., Cauley, G., Curtice, D., Fouad, A., Fink, L., Lauby, M. G., Wollenberg, B., Wrubel, J. N., “On-line power system security analysis” (Invited paper), Proceedings of the IEEE, v.80, n.2, pp.262280, Feb 1992
[23]Bergen, A. R., Hill, D. J., “A structure preserving model for power system stability analysis”, IEEE Transactions on Power Apparatus and Systems, v.100, pp.2535, 1981
[24]Bhatia, N. P., Szego, G. P., Stability Theory of Dynamical Systems, Springer-Verlag, 1970
[25]Blanchini, F., “Set invariance in control”, Automatica, v.35, pp.17471767, 1999
[26]Bondi, P., Casalino, G., Gambardella, L., “On the iterative learning control theory for robotic manipulators”, IEEE Journal of Robotics and Automation, v.4, n.1, pp.1422, Feb 1998
[27]Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, v.15, SIAM, Philadelphia, PA, 1994
[28]Brave, Y., Heymann, M., “On stabilization of discrete-event processes”, International Journal on Control, v.51, n.5, pp.11011117, 1990
[29]Bretas, N. G., Alberto, L. F. C., “Lyapunov function for power systems with transfer conductances: an extension of the invariance principle”, IEEE Transactions on Power Systems, v.18, n.2, pp.769777, May 2003
[30]Brockett, R. W., Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, Brockett, R. W., Millmann, R. S., and Sussmann, H. J., Eds., Progress in Mathematics, Birkhauser, Boston, MA, 1983
[31]Bronstein, I. U., Ya, A. K., Smooth Invariant Manifolds and Normal Forms, World Scientific, Singapore, 1994
[32]Burridge, R. R., Rizzi, A. A., Koditschek, D. E., “Sequential composition of dynamically dexterous robot behaviors”, International Journal of Robotics Research, v.18, n.6, pp.534555, Jun 1999
[33]Cabré, X., Fontich, E., de la Llave, R., “The parametrization method for invariant manifolds III. Overview and applications”, Journal of Differential Equations, v.218, n.2, pp.444515, 2005
[34]Cai, D., “Multiple equilibria and bifurcations in an economic growth model with endogenous carrying capacity”, International Journal of Bifurcation and Chaos, v.20, n.11, pp.34613472, 2010
[35]Chadalavada, V., Vittal, V., Ejebe, G. C., et al., “An on-line contingency filtering scheme for dynamic security assessment”, IEEE Transactions on Power Systems, v.12, n.1, pp.153161, Feb 1997
[36]Chang, K. W., “Two problems in singular perturbations of differential equations”, Journal of the Australian Mathematical Society, pp.3350, 1969
[37]Chen, Y., Chen, J., “Robust composite control for singularly perturbed systems with time-varying uncertainties”, Journal of Dynamic Systems Measurement and Control – Transactions of the ASME, v.117, n.4, pp.445452, Dec 1995
[38]Chen, Y. K., Schinzinger, R., “Lyapunov stability of multimachine power systems using decomposition-aggregation method”, Proc. IEEE -PES Winter Meeting, paper A 80036–4, 1980
[39]Chesi, G., “Estimating the domain of attraction for non-polynomial systems via lmi optimizations”, Automatica, v.45, n.6, pp.15361541, 2009
[40]Chesi, G., Domain of Attraction, Analysis and Control via SOS Programming, Lecture Notes in Control and Information Sciences, v.415, Springer-Verlag, London, 2011
[41]Chesi, G., Garulli, A., Tesi, A., Vicino, A., “LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems”, International Journal of Robust and Nonlinear Control, v.15, pp.3549, 2005
[42]Chesi, G., Tesi, A., Vicino, A., “Computing optimal quadratic Lyapunov functions for polynomial nonlinear systems via LMIs”, IFAC 15th Triennial World Congress, Barcelona, Spain, 2002
[43]Chiang, C. J., Stefanopoulou, A. G., Jankoviv, M., “Nonlinear observer-based control of load transitions in homogeneous charge compression ignition engines”, IEEE Transactions on Control Systems Technology, v.15, n.3, pp.438448, May 2007
[44]Chiang, H. D., “Analytical results on the direct methods for power system transient stability analysis”, Control and Dynamic Systems: Advances in Theory and Application, v.43, pp.275334, Academic Press, New York, 1991
[45]Chiang, H. D., Direct Methods for Stability Analysis of Electrical Power Systems: Theoretical Foundation, BCU Methodologies and Application, John Wiley & Sons, 2011
[46]Chiang, H. D., The BCU method for direct stability analysis of electric power systems: pp. theory and applications, Systems Control Theory for Power Systems, IMA Volumes in Mathematics and Its Applications, v.64, pp.3994, Springer-Verlag, New York, 1995
[47]Chiang, H. D., “Study of the existence of energy functions for power-systems with losses”, IEEE Transactions on Circuits and Systems, v.36, n.11, pp.14231429, Nov 1989
[48]Chiang, H. D., Chen, J. H., Reddy, C. K., Trust-Tech-based global optimization methodology for nonlinear programming. In Lectures on Global Optimization, Pardalos, P. M. and Coleman, T. F., Eds., American Mathematical Society, 2009
[49]Chiang, H. D., Chu, C.C., “A systematic search method for obtaining multiple local optimal solutions of nonlinear programming problems”, IEEE Transactions on Circuits and Systems: I, v.43, n.2, pp.99109, 1996
[50]Chiang, H. D., Chu, C. C.. “Theoretical foundation of the BCU method for direct stability analysis of network-reduction power system models with small transfer conductances”, IEEE Transactions on Circuits and Systems: I, v.42, n.5, pp.252265, May 1995
[51]Chiang, H. D., Chu, C. C., Cauley, G., “Direct stability analysis of electric power systems using energy functions: theory, applications and perspectives”, Proceedings of the IEEE, v.38, n.11, pp.14971529, Nov 1995
[52]Chiang, H. D., Conneen, T. P., Flueck, A.J., “Bifurcations and chaos in electric power systems: Numerical studies”, Journal of the Franklin Institute, v.331, n.6, pp.10011036, Nov1994
[53]Chiang, H. D., Fekih-Ahmed, L., “Quasi-stability regions of nonlinear dynamical systems: optimal estimation”, IEEE Transactions on Circuits and Systems: I, v.43, n.82, pp.636642, Aug 1996
[54]Chiang, H. D., Hirsch, M. W., Wu, F. F., “Stability region of nonlinear autonomous dynamical systems”, IEEE Transactions on Automatic Control, v.33, n.1, pp.1627, Jan 1988
[55]Chiang, H. D., Ku, B. Y., Thorp, J. S., “A constructive method for direct analysis of transient stability”, IEEE Proc. 27th Conf. on Decision Control, Austin, TX, pp.684689 Dec 1988
[56]Chiang, H. D., Lee, J., Trust-Tech paradigm for computing high-quality optimal solutions: method and theory. In Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems, Lee, K. Y. and El-Sharkawi, M. A., Eds., pp.209234, Wiley-IEEE Press, 2008
[57]Chiang, H. D., Liu, C. W., Varaiya, P. P., “Chaos in a simple power system”, IEEE Transactions on Power Systems, v.8, n.4, pp.14071417, Nov 1993
[58]Chiang, H. D., Subramanian, A. K., “BCU dynamic security assessor for practical power system models”, IEEE PES Summer Meeting, Edmonton, Alberta, July 18–22, pp.287293, 1999
[59]Chiang, H. D., Tada, Y., Li, H., Power system on-line transient stability assessment (invited chapter), Wiley Encyclopedia of Electrical and Electronics Engineering, John Wiley & Sons, New York, 2007
[60]Chiang, H. D., Thorp, J. S., “Stability regions of nonlinear systems: a constructive methodology”, IEEE Transactions on Automatic Control, v.34, n.12, pp.12291241, Dec 1989
[61]Chiang, H. D., Wang, T., Neighboring local-optimal solutions and its applications. In Optimization in Science and Engineering, Springer, pp.6788, 2014
[62]Chiang, H. D., Wang, B., Jiang, Q. Y., Applications of Trust-Tech methodology in optimal power flow of power systems. In Optimization in the Energy Industry, Springer, pp.297318, 2009
[63]Chiang, H. D., Wang, C. S., Li, H., “Development of BCU classifiers for on-line dynamic contingency screening of electric power systems”, IEEE Transactions on Power Systems, v.14, n.2, pp.660666, May 1999
[64]Chiang, H. D., Wu, F. F., Varaiya, P. P., “A BCU method for direct analysis of power system transient stability”, IEEE Transactions on Power Systems, v.8, n.3, pp.11941208, Aug 1994
[65]Chiang, H. D., Wu, F. F., Varaya, P. P., “Foundations of direct methods for power system transient stability analysis”, IEEE Transactions on Circuits and Systems, v.34, n.2, pp.160173, Feb 1987
[66]Chiang, H. D., Zheng, Y., Tada, Y., Okamoto, H., Koyanagi, K., Zhou, Y. C., “Development of on-line BCU dynamic contingency classifiers for practical power systems”, 14th Power System Computation Conference (PSCC), Spain, June 24–28, 2002
[67]Chow, J. H., Time-Scale Modeling of Dynamic Networks with Applications to Power Systems, Springer-Verlag, Berlin, 1982
[68]Chu, C. C., Chiang, H. D., “Constructing analytical energy functions for network-preserving power system models”, Circuits Systems and Signal Processing, v.24, n.4, pp.363383, 2005
[69]Chua, L. O., Deng, A.-C., “Impasse points. Part I: numerical aspects”, International Journal of Circuit Theory and Applications, v.17, n.2, pp.213235, Apr 1989
[70]Chua, L. O., Wu, C. W., Huang, A., Zhong, G., “A universal circuit for studying and generating chaos – part I: route to chaos”, IEEE Transactions on Circuits and Systems, v.40, n.10, pp.732744, Oct 1993
[71]Ciliz, K., Harova, A., “Stability regions of recurrent type neural networks”, Electronic Letters, v.28, n.11, pp.10221024, May 1992
[72]Cloosterman, M., van de Wouw, N., Heemels, W., Nijmeijer, H., “Stability of networked control systems with uncertain time-varying delays”, IEEE Transactions on Automatic Control, v.54, n.7, pp.15751580, Jul 2009
[73]Conley, C. C., Isolated Invariant Sets and the Morse Index, American Mathematical Society, Providence, RI, 1978
[74]Corless, M., Garofalo, F., Glielmo, L., “New results on composite control of singularly perturbed uncertain linear systems”, Automatica, v.29, n.2, pp.387400, Mar 1993
[75]Corless, M., Glielmo, L., “On the exponential stability of singularly perturbed systems”, SIAM Journal on Control and Optimization, v.30, n.6, pp.13381360, Nov 1992
[76]Coutinho, D. F., Bazanella, A. S., Trofino, A., Silva, A. S., “Stability analysis and control of a class of differential algebraic nonlinear systems”, International Journal of Robust and Nonlinear Control, v.14, n.16, pp.13011326, 2004
[77]Coutinho, D. F., da Silva, J. M. Gomes Jr., “Computing estimates of the region of attraction for rational control systems with saturating actuators”, IET Control Theory and Applications, v.4, n.3, pp.315325, 2008
[78]Coutinho, D. F., Souza, C. E., “Robust domain of attraction estimates for a class of uncertain discrete-time nonlinear systems”, 8th IFAC Symposium on Nonlinear Control Systems, Bologna, Italy, pp.185190, 2010
[79]da Cruz, J. J., Geromel, J. G., “Decentralized control design for a class of nonlinear discrete time systems”, Proc. 25th Conf. on Decision and Control, Athens, Greece, pp.11821183, 1986
[80]Davison, E. J., Kurak, E. M., “A computational method for determining quadratic Lyapunov functions for nonlinear systems”, Automatica, v.7, pp.627, 1971
[81]Davy, R. J., Hiskens, I. A., “Lyapunov functions for multimachine power systems with dynamic loads”, IEEE Transactions on Circuits and Systems: I, v.44, n.9, pp.796812, Sept 1997
[82]Dieudonne, J., Foundation of Modern Analysis, 2nd edn, Academic Press,New York, 1969
[83]Djukanovic, M., Sobajic, D., Pao, Y.-H., “Neural-net based tangent hypersurfaces for transient security assessment of electric power systems”, International Journal of Electrical Power and Energy Systems, v.16, n.6, pp.399408, 1994
[84]Dong, Y., Cheng, D., Oin, H., “Applications of a Lyapunov function with a homogeneous derivative”, IEE Proceedings Control Theory and Applications, v.150, n.3, pp.255260, May 2003
[85]Ejebe, G. C., Jing, C., Gao, B., Waight, J. G. Pieper, G., Jamshidian, F., Hirsch, P., “On-line implementation of dynamic security assessment at Northern States power company”, IEEE PES Summer Meeting, Edmonton, Alberta, July 18–22, pp.270272, 1999
[86]Ejebe, G. C., Tong, J., “Discussion of clarifications on the BCU method for transient stability analysis”, IEEE Transactions on Power Systems, v.10, n.1, pp.218219, Feb 1995
[87]Elaiw, A. M., Xia, X., “HIV dynamics: analysis and robust multirate MPC-based treatment schedules”, Journal of Mathematical Analysis and Applications, v.359, n.1, pp.285301, Nov 2009
[88]El-Kady, M. A., Tang, C. K., Carvalho, V. F., Fouad, A. A., Vittal, V., “Dynamic security assessment utilizing the transient energy function method”, IEEE Transactions on Power Systems, v.1, n.3, pp.284291, Aug 1986
[89]Electric Power Research Institute, User’s Manual for DIRECT 4.0, EPRI TR-105886s, Electric Power Research Institute, Palo Alto, CA, Dec 1995
[90]Ernst, D., Ruiz-Vega, D., Pavella, M., Hirsch, P., Sobajic, D., “A unified approach to transient stability contingency filtering, ranking and assessment”, IEEE Transactions on Power Systems, v.16, n.3, pp.435443, Aug 2001
[91]Fairén, V., Velarde, M. G., “Dissipative structure in a nonlinear reaction–diffusion model with a forward inhibition; stability of secondary multiple steady states”, Reports on Mathematical Physics, v.16, n.3, pp.421432, 1979
[92]Fallside, F., Patel, M. R., “Step-response behaviour of a speed-control system with a back-e.m.f. nonlinearity”, Proceedings of the IEEE, v.112, n.10, pp.19791984, Oct 1965
[93]Fenichel, N., “Geometric singular perturbation theory for ordinary differential equations”, Journal of Differential Equations, v.31, pp.5398, 1979
[94]Floudas, C. A., Pardalos, P. M., Recent Advances in Global Optimization, Princeton Series in Computer Science, Princeton, NJ, 1992
[95]Fouad, A. A., Vittal, V., Power System Transient Stability Analysis: Using the Transient Energy Function Method, Prentice-Hall, Englewood Cliffs, NJ, 1991
[96]Franks, J. H., Homology and Dynamical Systems, C.B.M.S. Regional Conf. Series in Mathematics, v.49, American Mathematical Society, Providence, RI, 1982
[97]Genesio, R., Tartaglia, M., Vicino, A., “On the estimation of asymptotic stability regions: state of the art and new proposals”, IEEE Transactions on Automatic Control, v.30, pp.747755, Aug 1985
[98]Genesio, R., Vicino, A., “Some results on the asymptotic stability of second-order nonlinear systems”, IEEE Transactions on Automatic Control, v.29, n.9, pp.857861, Sept 1984
[99]Genesio, R., Vicino, A., “New techniques for constructing asymptotic stability regions for nonlinear systems”, IEEE Transactions on Circuits and Systems, v.31, pp.574581, Jun 1984
[100]Glover, S. F., Modeling and Stability Analysis of Power Electronics Based Systems, PhD Thesis, Purdue University, 2003
[101]da Silva, J. M. G., Tarbouriech, S., “Anti-windup design with guaranteed region of stability: an LMI-based approach”, IEEE Transactions on Automatic Control, v.50, n.1, pp.106111, Jan 2005
[102]Gouveia, J. R. R. Jr., Amaral, F. M., Alberto, L. F. C., “Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of a supercritical Hopf equilibrium point”, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, v.23, n.12, 1350196, 2013
[103]Grammel, G., “Exponential stability of nonlinear singularly perturbed differential equations”, SIAM Journal on Control and Optimization, v.44, n.5, pp.17121724, 2005
[104]Grizzle, J. W., Kang, J. M., “Discrete-time control design with positive semi-definite Lyapunov functions”, System and Control Letters, v.43, pp.287292, 2001
[105]Grujic, L. T., “Uniform asymptotic stability of nonlinear singularly perturbed and large scale systems”, International Journal of Control, v.33, n.3, pp.481504, 1981
[106]Grune, L., Wirth, F., “Computing control Lyapunov functions via a Zubov type algorithm”, Proc. 39th Conf. on Decision and Control, Sydney, Australia, Dec 2000
[107]Guckenheimer, J., Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1993
[108]Guckeinheimer, J., Holmes, P., Nonlinear Oscillations, Dynamical System, and Bifurcations of Vector Fields, 1st edn., Springer-Verlag, New York, 1983
[109]Guillemin, V., Pollack, A., Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974
[110]Gunther, N., Hoffman, G. W., “Qualitative dynamics of a network model of regulation of the immune system: a rationale for the IgM to IgG switch”, Journal of Theoretical Biology, v.94, pp.815855, 1982
[111]Hahn, W., Stability of Motion, Springer-Verlag, New York, 1967
[112]Hale, J. K., Ordinary Differential Equations, Krieger, Huntington, NY, 1980
[113]Hale, J. K., Introduction to Functional Differential Equations, Applied Mathematical Sciences, v.99, Springer-Verlag, 1993
[114]Hale, J. K., Koçak, H., Dynamics and Bifurcations, Springer-Verlag, New York, 1991
[115]Halsey, K. M., Glover, K.. “Analysis and synthesis on a generalized stability region”, IEEE Transactions on Automatic Control, v.50, n.7, pp.9971009, Jul 2005
[116]Hartman, P., Ordinary Differential Equations, Wiley, New York, 1973
[117]Hartman, P., Ordinary Differential Equations, 2nd edn., Classics in Applied Mathematics, SIAM, 1982
[118]Hassan, M. A., Storey, C., “Numerical determination of domains of attraction for electrical power systems using the method of Zubov analysis”, International Journal of Control, v.34, pp.371381, 1981
[119]Henkelman, G., Johannesson, G., Jonsson, H., Methods for finding saddle points and minimum energy paths. In Progress on Theoretical Chemistry and Physics, Schwartz, S. D., Ed., Kluwer Academic, pp.269300, 2000
[120]Henrion, D., Tarbouriech, S., Garcia, G., “Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach”, IEEE Transactions on Automatic Control, v.44, n.11, pp.22302237, Nov 1999
[121]Hill, D. J., Mareels, I. M. Y., “Stability theory for differential/algebraic systems with applications to power systems”, IEEE Transactions on Circuits and Systems, v.37, n.11, pp.14161423, Nov 1990
[122]Hirsch, M. W.. Differential Topology, Springer-Verlag, New York, 1976
[123]Hirsch, M. W., Pugh, C. C., Shub, M., “Invariant manifolds”, Bulletin of the American Mathematical Society, v.76, n.5, pp.10151019, 1970
[124]Hirsch, M. W., Smale, S., Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York, 1974
[125]Hiskens, I., Davy, R., “Lyapunov function analysis of power systems with dynamic loads”, Proceedings of the 35th IEEE Conference on Decision and Control, v.4, pp.38703875, Dec 1996
[126]Hiskens, I., Hill, D., “Energy functions, transient stability and voltage behavior in power systems with nonlinear loads”, IEEE Transactions on Power Systems, v.4, n.4, pp.15251533, Oct 1989
[127]Hopfield, J. J., “Neurons, dynamics and computation”, Physics Today, v.47, pp.4046, Feb 1994
[128]Hsu, C. S., Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems, Applied Mathematical Sciences, v.64, Springer-Verlag, 1988
[129]Hsu, P., Sastry, S., “The effect of discretized feedback in a closed loop system”, Proc. 26th Conf. on Decision Control, Los Angeles, CA, pp.15181523, 1987
[130]Hu, X., “Techniques in the stability of discrete systems”, Control and Dynamic Systems, v.66, pp.153216, 1994
[131]Hurewicz, W., Hallman, H., Dimension Theory, Princeton University Press, Princeton, NJ, 1948
[132]IEEE Committee Report, “Transient stability test systems for direct methods”, IEEE Transactions on Power Systems, v.7, pp.3743, Feb 1992.
[133]Jadbabaie, A., Hauser, J., “On the stability of recending horizon control with a general terminal cost”, IEEE Transactions on Automatic Control, v.50, n.5, pp.674678, May 2005
[134]Jardim, J. L., Neto, C. S., Kwasnicki, W. T., “Design features of a dynamic security assessment system”, IEEE Power System Conf. and Exhibition, New York, October 13–16, 2004
[135]Jing, Z., Jia, Z., Gao, Y., “Research of the stability region in a power system”, IEEE Transactions on Circuits and Systems: I, v.50, n.2, pp.298304, Feb 2003
[136]Jocic, L. B., “On the attractivity of imbedded systems”, Automatica, v.17, pp.853860, 1980
[137]Johansen, T. A., “Computation of Lyapunov functions for smooth nonlinear systems using convex optimization”, Automatica, v.36, n.11, pp.16171626, Nov 2000
[138]Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966
[139]Kaufman, M., Thomas, R., “Model analysis of the bases of multistationarity in the humoral immune response”, Journal of Theoretical Biology, v.129, pp.141162, 1987
[140]Kellet, C. M., Teel, A. R., “Smooth-Lyapunov functions and robustness of stability for difference inclusions”, System and Control Letters, v.52, pp.395405, 2004
[141]Khait, Y., Panin, A., Averyanov, A., “Search for stationary points of arbitrary index by augmented Hessian method”, International Journal of Quantum Chemistry, v.54, n.6, pp.329336, 1995
[142]Khalil, H. K., Nonlinear Systems, 3rd edn., Prentice Hall, 2002
[143]Kim, J., “On-line transient stability calculator”, Final Report RP2206–1, EPRI, Palo Alto, CA, March 1994
[144]Klimushchev, A. I., Krasovskii, N. N., “Uniform asymptotic stability of systems of differential equations with a small parameter in the derivative terms”, Journal of Applied Mathematics and Mechanics, v.25, n.4, pp.680690, 1961
[145]Koditschek, D. E., “Exact robot navigation by means of potential functions: some topological considerations”, Proceedings of the IEEE International Conference on Robotics and Automation, v.4, pp.16, 1987
[146]Kokotovic, P., Singular Perturbation Techniques in Control Theory, Lecture Notes in Control and Information Sciences, v.90, pp.155, Springer, 1987
[147]Kokotovic, P., Marino, R.On vanishing stability regions in nonlinear systems with high-gain feedback”, IEEE Transactions on Automatic Control, v.31, n.10, pp.967970, Oct 1986
[148]Korobeinikov, A., “Stability of ecosystems: global properties of a general predator–prey model”, Mathematical Medicine and Biology, v.26, n.4, pp.309321, 2009
[149]Krasovskii, N. N., Problems of the Theory of Stability of Motion (In Russian, 1959), English translation, Stanford University Press, Stanford, CA, 1963
[150]Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer, J., Vladimirsky, A., Dellnitz, M., Junge, O., “A survey of methods for computing (un)stable manifolds of vector fields”, International Journal of Bifurcation and Chaos, v.15, n.3, pp.763791, 2005
[151]Kundur, P., Power System Stability and Control, McGraw Hill, New York, 1994
[152]Kuo, D.H., Bose, A., “A generation rescheduling method to increase the dynamics security of power systems”, IEEE Transactions on Power Systems, v.10, n.1, pp.6876, 1995.
[153]Kuznetsov, Y. A., Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1995
[154]Langson, W., Allevne, A., “A stability result with application to nonlinear regulation”, Journal of Dynamic Systems Measurement and Control – Transactions of the ASME, v.124, n.3, pp.452445, Sept 2002
[155]Laila, D. S., Lovera, M., Astolfi, A., “A discrete-time observer design for spacecraft attitude determination using an orthogonality-preserving algorithm”, Automatica, v.47, pp.975980, 2011
[156]LaSalle, J. P., Stability of Dynamical Systems, SIAM, Philadelphia, PA, 1976
[157]LaSalle, J. P., Stability Theory for Difference Equations, Studies in Ordinary Differential Equations, Studies in Mathematics, v.14, pp.131, Mathematical Association of America, Washington, DC, 1977
[158]LaSalle, J. P., “Some extensions of Liapunov’s second method”, IRE Transactions on Circuit Theory, v.7, pp.520527, 1960
[159]LaSalle, J. P., The Stability and Control of Discrete Processes, Springer-Verlag, New York, 1986
[160]La Salle, J. P., Lefschetz, S., Stability by Lyapunov’s Direct Method, Academic Press, New York, 1961
[161]Lee, J., Trajectory-based Methods for Global Optimization: Theory and Algorithms, PhD Dissertation, Department of Electrical Engineering, Cornell University, Ithaca, NY, 1999
[162]Lee, J., Chiang, H. D., “A dynamical trajectory-based methodology for systematically computing multiple optimal solutions of general nonlinear programming problems”, IEEE Transactions on Automatic Control, v.49, n.6, pp.888899, 2004
[163]Lee, J., Chiang, H. D., “Theory of stability regions for a class of nonhyperbolic dynamical systems and its application to constraint satisfaction problems”, IEEE Transactions on Circuits and Systems: I, v.49, n.2, pp.196209, 2002
[164]Levin, A., “An analytical method of estimating the domain of attraction for polynomial differential equations”, IEEE Transactions on Automatic Control, v.39, n.12, pp.24712475, Dec 1994
[165]Lewis, A., “An investigation of the stability in the large for an autonomous second-order two degree-of-freedom system”, International Journal of Non-Linear Mechanics, v.37, n.2, pp.153169, Mar 2002
[166]Liu, L., Tian, Y., Huang, X., A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to Biped Robots, Intelligent Robotics and Applications, pp.953962, Springer, 2008
[167]Llamas, A., De La, J. Lopez, R., Mili, L., Phadke, A. G., Thorp, J. S., “Clarifications on the BCU method for transient stability analysis”, IEEE Transactions Power Systems, v.10, n.1, pp.210219, Feb 1995
[168]Loccufier, M., Noldus, E., “A new trajectory reversing method for estimating stability regions of autonomous nonlinear systems”, Nonlinear Dynamics, v.21, pp.265288, 2000
[169]Luxemburg, L. A., Huang, G., “On the number of unstable equilibria of a class of nonlinear systems”, 26th IEEE Conf. on Decision Control, pp.889894, 1987.
[170]Luyckx, L., Loccufier, M., Noldus, E., “Computational methods in nonlinear stability analysis: stability boundary calculations”, Journal of Computational and Applied Mathematics, v.168, n.1–2, pp.289297, 2004
[171]Mansour, Y., Vaahedi, E., Chang, A. Y., Corns, B. R., Garrett, B. W., Demaree, K., Athay, T., Cheung, K., “B.C.Hydro’s on-line transient stability assessment (TSA) model development, analysis and post-processing”, IEEE Transactions on Power Systems, v.10, n.1, pp.241253, Feb 1995
[172]Magnusson, P. C., “Transient energy method of calculating stability”, AIEE Transactions, v.66, pp.747755, 1947
[173]O’Malley, R. E. Jr. Singular Perturbation Methods for Ordinary Differential Equations, Applied Mathematical Series, v.89, Springer-Verlag, 1991
[174]Marcus, C. M., Westervelt, R. M., “Dynamics of iterated-map neural networks”, Physics Review A, v.40, n.1, pp.501504, 1989
[175]Margolis, S. G., Vogt, W. G., “Control engineering applications of V. I. Zubov’s construction procedure for Lyapunov functions”, IEEE Transactions on Automatic Control, v.8, pp.104113, Apr 1963
[176]May, R. M., Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1973
[177]Mazumder, S. K., Nayfeh, A. H., Borojevic, D., “A nonlinear approach to the analysis of stability and dynamics of standalone and parallel dc-dc converters”, Proc. Applied Power Electronics Conference and Exposition, pp.784790, 2001
[178]Mercede, F., Chow, J. C., Yan, H., Fishl, R., “A framework to predict voltage collapse in power systems”, IEEE Transactions on Power Systems, v.3, n.4, pp.18071813, Nov 1988
[179]Meza, J. L., Santibanez, V., Campa, R., “An estimate of the domain of attraction for the PID regulator of manipulators”, International Journal of Robotics and Automation, v.22, n.3, pp.187195, 2007
[180]Michel, A. N., Miller, R. K., Qualitative Analysis of Large Scale Dynamical Systems, Academic Press, New York, 1977
[181]Michel, A. N., Miller, R. K., Nam, B. H., “Stability analysis of interconnected systems using computer generated Lyapunov functions”, IEEE Transactions on Circuits and Systems, v.29, pp.431440, Jul 1982
[182]Michel, A. N., Sarabudla, N. R., Miller, R. K., “Stability analysis of complex dynamical systems: some computational methods”, Circuits, Systems and Signal Processing, v.l, pp.171202, 1982
[183]Milani, B. E. A., “Contractive polyhedra for discrete time linear systems with saturating controls”, Proceedings of the 38th IEEE Conference on Decision and Control, pp.20392044, Dec 1999
[184]Miller, R. K., Michel, A. N., Ordinary Differential Equations, Academic Press, New York, 1982
[185]Milnor, J., “On the concept of attractor”, Communications in Mathematical Physics, v.99, pp.177195, 1985
[186]Milnor, J., Topology from the Differential Viewpoint, University of Virginia Press, 1965
[187]Min, Y., Chen, L., Hou, K., Song, Y., “The credible regions on the approximate stability boundaries of nonlinear dynamic systems”, IEEE Transactions on Automatic Control, v.52, n.8, pp.14861491, 2007
[188]Mira, C., Fournier-Prunaret, D., Gardini, L., Kawakami, H., Cathala, J. C., “Basin bifurcations of two-dimensional noninvertible maps: fractalization of basins”, International Journal of Bifurcation and Chaos, v.4, n.2, pp.343381,1994
[189]Miron, R., Fichthorn, K., “The step and slide method for finding saddle points on multidimensional potential surfaces”, Journal of Chemical Physics, v.115, n.19, pp.87428747, 2001
[190]Mokhtari, S., et al., Analytical methods for contingency selection and ranking for dynamic security assessment, Final Report RP3103–3, EPRI, Palo Alto, CA, May 1994
[191]Morse, M., The Calculus of Variations in the Large, American Mathematical Society, 1934
[192]Munkres, J. R.. Topology – A First Course, Prentice- Hall, Englewood Cliffs, NJ, 1975
[193]Munkres, J. R., Topology, 2nd edn., Prentice-Hall, 2000
[194]Nicolaescu, L. I., An Invitation to Morse Theory, Springer, 2007
[195]Noldus, E., Spriet, J., Verriest, E., Van Cauwenberghe, A., “A new Lyapunov technique for stability analysis of chemical reactors”, Automatica, v.10, n.6, pp.675680, Dec 1974
[196]Ortega, R., Loria, A., Kelly, R., “A semiglobally stable output feedback PI2D regulator for robot manipulators”, IEEE Transactions on Automatic Control, v.40, n.8, pp.14321436, Aug 1995
[197]Paganini, F., Lesieutre, B.C., A critical review of the theoretical foundations of the BCU method, Technical Report TR97-005, MIT Lab., Electromagnetic and Electrical Systems, July 1997
[198]Paganini, F., Lesieutre, B.C., “Generic properties, one-parameter deformations, and the BCU method”, IEEE Transactions on Circuits and Systems: I, v.46, n.6, pp.760763, Jun 1999
[199]Pai, M. A., Energy Function Analysis for Power System Stability, Kluwer Academic Publishers, Boston, MA, 1989
[200]Palis, J., “On Morse–Smale dynamical systems”, Topology, v.8, pp.385405, 1969.
[201]Palis, J., de Melo, J. W., Geometric Theory of Dynamical Systems: An Introduction, Springer-Verlag, New York, 1981
[202]Palis, J., Melo, W., Introdução aos Sistemas Dinâmicos, Edgard Blucher, 1978
[203]Peixoto, M. M., “On an approximation theorem of Kupka and Smale”, Journal of Differential Equations, v.3, n.2, pp.214227, Apr 1967
[204]Peponides, G., Kokotovic, P. V., Chow, J. H., “Singular perturbations and time scales in nonlinear models of power systems”, IEEE Transactions on Circuits and Systems, v.29, n.11, pp. 758767, Nov 1982
[205]Perko, L., Differential Equations and Dynamical Systems, Springer, New York, 1991
[206]Peterman, R. M., “A simple mechanism that causes collapsing stability regions in exploited salmonid populations”, Journal of the Fisheries Research Board of Canada, v.34, pp.11301142, 1977
[207]Praprost, K., Loparo, K. A., “A stability theory for constrained dynamic systems with applications to electric power systems”, IEEE Transactions on Automatic Control, v.41, n.11, pp.16051617, Nov 1996
[208]Psiaki, M. L., Luh, Y. P., “Nonlinear system stability boundary approximation by polytopes in state-space”, International Journal of Control, v.57, n.1, pp.197224, Jan 1993
[209]Pugh, C. C., “On a theorem of Hartman”, American Journal of Mathematics, v.91 n.2, pp.363367, 1969
[210]Quapp, W., Hirsch, M., Imig, O., Heidrich, D., “Searching for saddle points of potential energy surfaces by following a reduced gradient”, Journal of Computational Chemistry, v.19, pp.10871100, 1998
[211]Rabelo, M., Alberto, L. F. C., “An extension of the invariance principle for a class of differential equations with finite delay”, Advances in Difference Equations, article ID 496936, pp.14, 2010
[212]Rahimi, F. A., Lauby, M. G., Wrubel, J. N., Lee, K. L., “Evaluation of the transient energy function method for on-line dynamic security assessment”, IEEE Transactions on Power Systems, v.8, n.2, pp.497507, May 1993
[213]Reddy, C., Chiang, H. D., “Finding Saddle points using stability boundaries”, Proc. 2005 ACM Symp. on Applied Computing, pp.212213, 2005
[214]Reddy, C., Chiang, H. D., “A stability boundary based method for finding saddle points on potential energy surfaces”, Journal of Computational Biology, v.13, n.3, pp.745766, Apr 2006
[215]Riverin, L., Valette, A., “Automation of security assessment for Hydro-Quebec’s power system in short-term and real-time modes”, International Conference on Large High Voltage Electric Systems CIGRE, pp.39103, 1998
[216]Robinson, C., Dynamic Systems. Stability, Symbolic Dynamics and Chaos, 2nd edn., CRC Press, 1998
[217]Rodriguez, H., Ortega, R., Escobar, G., Barabanov, N., “A robustly stable output feedback saturated controller for the boost DC-to-DC converter”, Systems and Control Letters, v.40, n.1, pp.18, 2000
[218]Rodrigues, H. M., Alberto, L. F. C., Bretas, N. G., “On the invariance principle: generalizations and applications to synchronization”, IEEE Transactions on Circuits and Systems: I, v.47, n.5, pp.730739, May 2000
[219]Rodrigues, H. M., Wu, J. H., Gabriel, L. R. A., “Uniform dissipativeness, robust synchronization and location of the attractor of parametrized nonautonomous discrete systems”, International Journal of Bifurcation and Chaos, v.21, n.2, pp.513526, 2011
[220]Rudin, W., Principles of Mathematical Analysis, International Series in Pure and Applied Mathematics, 3rd edn., McGraw-Hill, 1976
[221]Saberi, A., Khalil, H., “Quadratic-type Lyapunov functions for singularly perturbed systems”, IEEE Transactions on Automatic Control, v.29, n.6, pp.542550, Jun 1984
[222]Saeki, M., Araki, M., “A new estimate of the stability regions of large-scale systems”, International Journal of Control, v.32, n.2, pp.257269, 1980
[223]Sasaki, H., “An approximate incorporation of field flux decay into transient stability analysis of multimachine power systems by the second method of lyapunov”, IEEE Transactions on Power Apparatus and Systems, v.98, n.2, pp.473483, Mar–Apr 1979
[224]Sauer, P. W., Pai, M. A., Power System Dynamics and Stability, Prentice-Hall, Englewood Cliffs, NJ 1998
[225]Segel, L. A., “Multiple attractors in immunology: theory and experiment”, Biophysical Chemistry, v.72, pp.223230, 1998
[226]Shields, D. N., Storey, C., “The behavior of optimal Lyapunov functions”, International Journal of Control, v.21, n.4, pp.561573, 1975
[227]Shim, H., Seo, J. H., “Non-linear output feedback stabilization on a bounded region of attraction”, International Journal of Control, v.73, n.5, pp.416426, Mar 2000
[228]Shub, M., Global Stability of Dynamical Systems, Springer-Verlag, New York, 1987
[229]Siqueira, A. A. G., Terra, M. H., “Nonlinear H-infinity control applied to biped robots”, Proceedings of the 2006 IEEE International Conference on Control Applications, Munich, Germany, Oct 2006
[230]Shyu, K. K., Chen, S. R., “Estimation of asymptotic stability region and sliding domain of uncertain variable structure systems with bounded controllers”, Automatica, v.32, n.5, pp.797800, 1996
[231]Siddiqee, M. W., “Transient stability of an a.c. generator by Lyapunov’s direct method”, International Journal of Control, v.8, n.2, pp.131144, 1968
[232]Šiljak, D. D., Large-Scale Dynamic Systems: Stability and Structure, North-Holland, New York, 1978
[233]Silva, F. H. J. R., Alberto, L. F. C., London, J. B. A. Jr., Bretas, N. G., “Smooth perturbation on a classical energy function for lossy power system stability analysis”, IEEE Transactions on Circuits and Systems: I, v.52, n.1, pp.222229, Jan 2005
[234]Smale, S., “Differential dynamical systems”, Bulletin of the American Mathematical Society, v.73, pp.747817, 1967
[235]Smith, K. T., Primer of Modern Analysis, Springer -Verlag, New York, 1983
[236]Sotomayor, J., Generic bifurcations of dynamical systems. In Dynamical Systems, Peixoto, M. M., Ed., pp.549560, Academic Press, New York, 1973
[237]Steward, G. W., Introduction to Matrix Computation, Academic Press, New York, 1973
[238]Stott, B., “Power system dynamic response calculations”, Proceedings of the IEEE, v.67, pp.219241, 1979
[239]Strang, G., Introduction to Linear Algebra, Wellesley-Cambridge Press, 1994
[240]Susuki, Y., Hikihara, T., Chiang, H. D., “Stability boundaries analysis of electric power system with dc transmission based on differential-algebraic equation system”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, v.E87-A, n.9, pp.23392346, Sept 2004
[241]Tada, Y., Chiang, H. D., “Design and implementation of on-line dynamic security assessment”, IEEJ Transactions on Electrical and Electronic Engineering, v.4, n.3, pp.313321, 2008
[242]Tada, Y., Kurita, A., Zhou, Y. C., Koyanagi, K., Chiang, H. D., Zheng, Y., “BCU-guided time-domain method for energy margin calculation to improve BCU-DSA system”, IEEE/PES Transmission and Distribution Conference and Exhibition, 2002
[243]Tada, Y., Takazawa, T., Chiang, H. D., Li, H., Tong, J., “Transient stability evaluation of a 12,000-bus power system data using TEPCO-BCU”, 15th Power System Computation Conference (PSCC), Belgium, Aug 2005
[244]Tada, Y., Ono, A., Kurita, A., Takahara, Y., Shishido, T., Koyanagi, K., “Development of analysis function for separated power system data based on linear reduction techniques on integrated power system analysis package”, 15th Conference of the Electric Power Supply, Shanghai, China, Oct 2004
[245]Takegaki, M., Arimoto, S., “A new feedback method for dynamic control of manipulators”, Journal of of Dynamic Systems, Measurement, and Control, v.103, n.2, pp.119125, Jun 1981
[246]Takens, F., Constrained equations; a study of implicit differential equations and their discontinuous solutions. In Structural Stability, the Theory of Catastrophes, and Applications in the Sciences, Lecture Notes in Mathematics, v.525, pp.143234, Springer, Berlin, 1976
[247]Tan, W., Packard, A., “Stability region analysis using polynomial and composite polynomial Lyapunov function and sum-of-squares programming”, IEEE Transactions on Automatic Control, v.53, n.2, pp.565571, Mar 2008
[248]Thom, R., Structural Stability and Morphogenesis, Benjamin, Reading, MA, 1975
[249]Thomas, R. J., Thorp, J. S., “Towards a direct test for large scale electric power system instabilities”, IEEE Proc. 24th Conf. on Decision and Control, Fort Lauderdale, FL, pp.6569, Dec 1985
[250]Tibken, B., “Estimation of the domain of attraction for polynomial systems via LMI’s”, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, Dec 2000
[251]Tong, J., Chiang, H. D., Conneen, T. P., “A sensitivity-based BCU method for fast derivation of stability limits in electric power systems”, IEEE Transactions on Power Systems, v.8, n.4, pp.14181437, 1993
[252]Topcu, U., Packard, A., Seiler, P., Wheeler, T., “Stability region analysis using simulations and sum-of-squares programming”, Proceedings of the 2007 American Control Conference, New York, Jul 2007
[253]Toussaint, G. J., Basar, T., “Achieving nonvanishing stability regions with high gain cheap control using H techniques: the second-order case”, Systems and Control Letters, v.44, n.2, pp.7989, Oct 2001
[254]Tsolas, N., Arapostathis, A., Varaiya, P., “A structure preserving energy function for power system transient stability analysis”, IEEE Transactions on Circuits and Systems, v.32, n.10, pp.10411050, Oct 1985
[255]Ushiki, S., “Analytic expressions of the unstable manifolds”, Proceedings of the Japan Academy, Series A, v.56, pp.239243, 1980
[256]Vannelli, A., Vidyasagar, M., “Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems”, Automatica, v.21, n.1, pp.6980, 1985
[257]Varaiya, P. P., Wu, F. F., Chen, R. L., “Direct methods for transient stability analysis of power systems: recent results”, Proceedings of the IEEE, v.73, pp.17031715, Dec 1985
[258]Varghese, M., Thorp, J. S., “An analysis of truncated fractal growths in the stability boundaries of three-node swing equations”, IEEE Transactions on Circuits and Systems, v.35, pp.825834, 1988
[259]Vasil’eva, A. B., Butuzov, V. F., Asymptotical Expansions of the Solutions of Singularly Perturbed Systems, Nauka, Moscow, 1973
[260]Vasil’eva, A. B., Butuzov, V. F., Kalachev, L. V., The Boundary Function Method for Singular Perturbation Problems, SIAM, Philadelphia, PA, 1995
[261]Veliov, V., “A generalization of the Tikhonov theorem for singularly perturbed differential inclusions”, Journal of Dynamical and Control Systems, v.3, n.3, pp.291319, 1997
[262]Venkatasubramanian, V., A Taxonomy of the Dynamics of Large Differential-Algebraic Systems such as the Power Systems, PhD Thesis, Washington University, Sever Institute of Technology, 1992
[263]Venkatasubramanian, V., Ji, W., “Coexistence of four different attractors in a fundamental power system model”, IEEE Transactions on Circuits and Systems: I, v.46, n.3, pp.405409, Mar 1999
[264]Venkatasubramanian, V., Schattler, H., Zaborsky, J., “Dynamic of large constrained nonlinear systems – a taxonomy theory”, Proceedings of the IEEE, v.83, n.11, pp.15301560, Nov 1995
[265]Vidyasagar, M., Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1978
[266]Vidyasagar, M., “New directions of research in nonlinear system theory”, Proceedings of the IEEE, v.74, pp.10601091, Aug 1986
[267]Villafuerte, R., Mondié, S., “Estimate of the region of attraction for a class of nonlinear time delay systems: a leukemia post-transplantation dynamics example”, Proc. 46th IEEE Conference on Decision and Control, New Orleans, LA, pp.633638, Dec 2007
[268]Villafuerte, R., Mondié, S., Niculescu, S. I., “Stability analysis and estimate of the region of attraction of a human respiratory model”, Proc. 47th IEEE Conference on Decison and Control, Mexico, pp.26442649, 2008
[269]Vournas, C. D., Sakelladaridis, N., “Region of attraction in a power system with discrete ltcs”, IEEE Transactions on Circuits and Systems: I, v.53, n.7, pp.16101618, Jul 2006
[270]Wada, N., et al., “Model predictive tracking control using a state-dependent gain-schedule feedback”, Proc. 2010 Int. Conf. on Modelling, Identification and Control, Japan, pp.418423, 2010
[271]Wang, L., Morison, K., “Implementation of on-line security assessment”, IEEE Power and Energy Magazine, v.4, n.5, Sept/Oct 2006
[272]Wang, W. X., Zhang, Y. B., Liu, C. Z., “Analysis of a discrete-time predator-prey system with allee effect”, Ecological Complexity, v.8, n.1, pp.8185, 2011
[273]Weissenberger, S., “Stability regions of large-scale systems”, Automatica, v.9, pp.653663, 1973
[274]Westervelt, E. R., Grizzle, J. W., de Wit, C. C., “Switching and PI control of walking motions of planar biped walkers”, IEEE Transactions on Automatic Control, v.48, n.2, pp.308312, Feb 2003
[275]Westervelt, E. R., Grizzle, J. W., Koditschek, D. E., “Hybrid zero dynamics of planar biped walkers”, IEEE Transactions on Automatic Control, v.48, n.1, pp.4256, Jan 2003
[276]Wiggins, S., Global Bifurcations and Chaos: Analytical Methods, Applied Mathematical Sciences, v.73, Springer-Verlag, New York, 1988
[277]Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, 1990
[278]Wimmer, H. K., “Inertia theorem for matrices, controllability, and linear vibration”, Linear Algebra and its Applications, v.8, pp.337343, 1974
[279]Xin, H., Gan, D., Huang, M., Wang, K., “Estimating the stability region of singular perturbation power systems with saturation nonlinearities: an LMI-based method”, IET Control Theory and Applications, v.4, n.3, pp.351361, 2010
[280]Xin, H., Gan, D., Qiu, J., Qu, Z., “Methods for estimating stability regions with application to power systems”, European Transactions on Electric Power, v.17, n.2, pp.113133, Mar/Apr 2007
[281]Xu, D., Li, S., Pu, Z., Guo, Q., “Domain of attraction of nonlinear discrete systems with delays”, Computers and Mathematics with Applications, v.38, pp.155162, 1999
[282]Yee, H., Spalding, B. D., “Transient stability analysis of multi-machine systems by the method of hyperplanes”, IEEE Transactions on Power Apparatus and Systems, v.96, n.1, pp.276284, Jan 1977
[283]Yu, T., Yu, J., Li, H., Lin, H., “Complex dynamics of industrial transferring in a credit-constrained economy”, Physics Procedia, v.3, n.5, pp.16771685, 2010
[284]Yu, Y., Vongsuriya, K., “Nonlinear power system stability study by Lyapunov function and Zubov’s methodIEEE Transactions on Power Apparatus and Systems, v.86, pp.14801485, 1967
[285]Zaborszky, J., Huang, G., Zheng, B., Leung, T. C., “On the phase portrait of a class of large nonlinear dynamic systems such as the power system”, IEEE Transactions on Automatic Control, v.33, n.1, pp.415, Jan 1988
[286]Zadeh, L. A., Desoer, C. A., Linear System Theory – The State Space Approach, McGraw-Hill, New York, 1963
[287]Zhong, J., et al., “New results on non-regular linearization of non-linear systems”, International Journal of Control, v.80, n.10, pp.16511664, 2007
[288]Zou, Y., Yin, M. H., Chiang, H. D., “Theoretical foundation of the controlling UEP method for direct transient stability analysis of network-preserving power system models”, IEEE Transactions on Circuits and Systems, v.50, n.10, pp.13241336, Oct 2003