Antoulas, A. C. 2005 Approximation of Large-Scale Dynamical Systems. Advances in Design and Control. SIAM.
Antoulas, A. C., Sorensen, D. C. & Gugercin, S. 2001 A survey of model reduction methods for large-scale systems. Contemp. Math. 280, 193–219.
Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.
Bangia, A. K., Batcho, P. F., Kevrekidis, I. G. & Karniadakis, G. E. 1997 Unsteady two-dimensional flows in complex geometries: comparative bifurcation studies with global eigenfunction expansions. SIAM J. Sci. Comput. 18, 775–805.
Bergmann, M., Cordier, L. & Brancher, J.-P. 2005 Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model. Phys. Fluids 17 (9), 097101:1–21.
Borggaard, J. & Burns, J. 1997 A PDE sensitivity equation method for optimal aerodynamic design. A PDE sensitivity equation method for optimal aerodynamic design 136 (2), 367–384.
Borggaard, J., Hay, A. & Pelletier, D. 2007 Interval-based reduced-order models for unsteady fluid flow. Interval-based reduced-order models for unsteady fluid flow 4 (3–4), 353–367.
Couplet, M., Basdevant, C. & Sagaut, P. 2005 Calibrated reduced-order POD-Galerkin system for fluid flow modeling. Calibrated reduced-order POD-Galerkin system for fluid flow modeling 207 (1), 192–220.
Davis, R. W. & Moore, E. F. 1982 A numerical study of vortex shedding from rectangles. J. Fluid Mech. 116, 475–506.
Deane, E. A., Kevrekidis, I. G., Karniadakis, G. E. & Orszag, S. A. 1991 Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys. Fluids A 3 (10), 2337–2354.
Fahl, M. 2000 Trust-region methods for flow control based on reduced order modelling. PhD thesis, Universität Trier, Germany.
Fox, R. L. & Kapoor, M. P. 1968 Rates of change of eigenvalues and eigenvectors. AIAA J. 6 (12), 2426–2429.
Franke, R., Rodi, W. & Schoaconung, B. 1990 Numerical calculation of laminar vortex-shedding flow past cylinders. J. Wind Engng Ind. Aerodyn. 35, 237–257.
Galletti, B., Bruneau, C. H., Zannetti, L. & Iollo, A. 2004 Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 503, 161–170.
Ganapathysubramanian, S. & Zabaras, N. 2004 Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties. Comput. Meth. Appl. Mech. Engng 193, 5017–5034.
Graham, W. R., Peraire, J. & Tang, K. T. 1999 a Optimal control of vortex shedding using low order models. Part 1. Open-loop model development. Intl J. Numer. Methods Engng 44 (7), 945–972.
Graham, W. R., Peraire, J. & Tang, K. T. 1999 b Optimal control of vortex shedding using low order models. Part 2. Model-based control. Intl J. Numer. Methods Engng 44 (7), 973–990.
Hay, A., Borggaard, J. & Pelletier, D. 2008 On the use of sensitivity analysis to improve reduced-order models. In 4th AIAA Flow Control Conference, Seattle, Washington, AIAA-2008–4192.
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University.
Hotelling, H. 1933 Analysis of a complex of statistical variables with principal components. J. Educat. Psych. 24, 417–441.
Hristova, H., Etienne, S., Pelletier, D. & Borggaard, J. 2006 A continuous sensitivity equation method for time-dependent incompressible laminar flows. A continuous sensitivity equation method for time-dependent incompressible laminar flows 50 (7), 817–844.
Ilinca, F., Pelletier, D. & Hay, A. 2008 First- and second-order sensitivity equation methods for value and shape parameters. First- and second-order sensitivity equation methods for value and shape parameters 57 (9), 1349–1370.
Ito, K. & Ravindran, S. 1996 Reduced basis method for flow control. Tech Rep. CRSC-TR96-25, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC.
Karhunen, K. 1946 Zur Spektraltheorie stochastischer Prozesse. Zur Spektraltheorie stochastischer Prozesse 37.
Kunisch, K. & Volkwein, S. 1999 Control of Burgers' equation by a reduced order approach using proper orthogonal decomposition. J. Optim. Theor. Appl. 102, 345–371.
Kunisch, K., Volkwein, S. & Xie, L. 2004 HJB-POD-based feedback design for the optimal control of evolution problems. SIAM J. Appl. Dyn. Syst. 3 (4), 701–722.
Lancaster, P. 1964 On eigenvalues of matrices dependent on a parameter. Numer. Math. 6, 377–387.
Lehmann, O., Luchtenburg, D. M., Noack, B. R., King, R., Morzyński, M. & Tadmor, G. 2005 Wake stabilization using POD Galerkin models with interpolated modes. In 44th IEEE Conference on Decision and Control (CDC) and European Control Conference (ECC), Sevilla, Spain.
Lieu, T., Farhat, C. & Lesoinne, M. 2006 Reduced-order fluid/structure modeling of a complete aircraft configuration. Comput. Meth. Appl. Mech. Engng 195, 5730–5742.
Loève, M. 1955 Probability Theory. Van Nostrand.
Lorenz, E. N. 1956 Empirical orthogonal functions and statistical weather prediction. Tech Rep. M.I.T.
Ma, X. & Karniadakis, G. E. 2002 A low-dimensional model for simulating three-dimensional cylinder flow. J. Fluid Mech. 458, 181–190.
Morzyński, M., Afanasiev, K. & Thiele, F. 1999 Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. Comput. Meth. Appl. Mech. Engng 169, 161–176.
Morzyński, M., Stankiewicz, W., Noack, B. R., King, R., Thiele, F. & Tadmor, G. 2007 Continuous mode interpolation for control-oriented models of fluid flows. In Active Flow Control (ed. King, R.), pp. 260–278. Springer-Verlag.
Murthy, D. V. & Haftka, R. T. 1988 Derivatives of eigenvalues and eigenvectors of a general complex matrix. Intl J. Numer. Meth. Engng 26, 293–311.
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.
Noack, B. R. & Eckelmann, H. 1994 a A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297–330.
Noack, B. R. & Eckelmann, H. 1994 b A low-dimensional Galerkin method for the three-dimensional flow around a ciruclar cylinder. Phys. Fluids 6, 124–143.
Okajima, A. 1982 Strouhal number of rectangular cylinders. J. Fluid Mech. 123, 379–398.
Pelletier, D., Hay, A., Etienne, S. & Borggaard, J. 2008 The sensitivity equation method in fluid mechanics. The sensitivity equation method in fluid mechanics 17 (1–2), 31–61.
Peterson, J. S. 1989 The reduced basis method for incompressible viscous flow calculations. The reduced basis method for incompressible viscous flow calculations 10 (4), 777–786.
Rowley, C. W. & Williams, D. R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251–276.
Saha, A. K., Biswas, G. & Muralidhar, K. 2003 Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Intl J. Heat Fluid Flow 24, 54–66.
Seyranian, A. P., Lund, E. & Olhoff, N. 1994 Multiple eigenvalues in structural optimization problems. Struct. Optim. 8, 207–227.
Sirisup, S. & Karniadakis, G. E. 2004 A spectral viscosity method for correcting the long-term behavior of POD models. J. Comput. Phys. 194, 92–116.
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I. Coherent structures. Turbulence and the dynamics of coherent structures. Part I. Coherent structures 45 (3), 561–571.
Sohankar, A., Norberg, C. & Davidson, L. 1997 Numerical simulation of unsteady low-Reynolds number flow around rectangular cylinders at incidence. J. Wind Engng Ind. Aerodyn. 69–71, 189–201.
Sohankar, A., Norberg, C. & Davidson, L. 1998 Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition. Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition 26 (1), 39–56.
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers 11 (2), 189–201.