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The structure of the singularities of holomorphic matrices

Published online by Cambridge University Press:  14 November 2011

L. Pandolfi
L. Pandolfi
Affiliation:
Politecnico di Torino, Dipartimento di Matematica, C. so Duca degli Abruzzi 24, 10129-Turin, Italy
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Synopsis

In this paper we consider a holomorphic matrix H(z) over a possibly unbounded region Ω and we study its properties in the neighbourhoods of a boundary point z0 of Ω (it may be z0 = ∞ if Ω is unbounded and z0 may not be an isolated singularity). Applications to systems theory and, in particular, to the theory of delay systems are presented. In this case the properties of completability, small solutions observability and zeros at z0 = ∞ are investigated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 1 - 14
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Banks, S. P.. State-space and frequency-domain methods in the control of distributed parameter systems (London: P. Peregrinus Ltd, 1983).Google Scholar
2Bart, H., Gohberg, I. and Kaashoek, M. A.. Minimal factorization of matrix operators functions (Basel: Birkhauser, 1979).CrossRefGoogle Scholar
3Bart, H., Kaashoek, M. A. and Lay, D. C.. The integral formula for the reduced algebric multiplicity of meromorphic operator functions. Proc. Edinburgh Math. Soc. 21 (1978), 65–72.CrossRefGoogle Scholar
4Conte, G. and Perdon, A. M.. Infinite zero module and infinite pole module. In Analysis and optimization of systems, eds. Bensoussan, A. and Lions, J. P., pp. 302–315 (Berlin: Springer, 1984.)CrossRefGoogle Scholar
5Henry, D.. Small solutions of linear autonomous functional differential equations. J. Differential Equations 18 (1970), 495–501.Google Scholar
6Kappel, F. and Wimmer, H. K.. An elementary divisor theory for autonomous linear functional differential equations. J. Differential Equations 21 (1976), 134–147.CrossRefGoogle Scholar
7Danilevski, J. A. Lappo. Memoires sur la theorie des systemes des equationes differentielles lineaires (New York: Chelsea Publishing Company, 1953).Google Scholar
8Manitius, A.. Completeness and F-Completeness of eigenfunctions associated with retarded functional differential equations. J. Differential Equations 35 (1980) 1–29.CrossRefGoogle Scholar
9Manitius, A.. Necessary and sufficient conditions of approximate controllability for general linear retarded systems. SIAM J. Control Optim. 19 (1981) 516–532.CrossRefGoogle Scholar
10Pandolfi, L.. The transmission zeros of systems with delays. Internat. J. Control 36 (1982) 959–976.CrossRefGoogle Scholar
11Pandolfi, L.. The pole and zero structure of a class of linear systems. In Control theory for distributed parameter systems and applications, eds. Kappel, F., Kunisch, K. and Schappacher, W., pp. 163–174 (Berlin: Springer, 1983).CrossRefGoogle Scholar
12Pandolfi, L.. Tandem connection of systems with delays. Proceedings of the II conference on Control theory for distributed parameter systems and applications, eds. Kappel, F., Kunish, K. and Schappacher, W., pp. 262–279 (Berlin: Springer, 1985).Google Scholar
13Pandolfi, L.. Interconnected systems with delays. In Frequency domain and state space methods for linear systems, eds. Byrnes, C. I. and Lindqvist, A., pp. 407–422 (Amsterdam: North-Holland, 1986).Google Scholar
14Postlethwaite, I. and MacFarlane, A. G. J.. A complex variable approach to the analysis of linear multivariable feedback systems (Berlin: Springer, 1979).CrossRefGoogle Scholar
15Schumaker, J. M.. Residue formula for meromorphic matrices. Proceedings of the VII conference on mathematical theory of network and systems (to appear).Google Scholar
16Sneddon, I. N.. The use of integral transforms (New Delhi: Tata-McGraw Hill, 1974).Google Scholar
17Thijsse, G. P. A.. On the (sub)logarithmic property of the pole-, zero- and algebraic multiplicity of operator functions. Proc. Edinburgh Math. Soc. (2) 23 (1980), 207–217.CrossRefGoogle Scholar
18Vidyasagar, M.. Control system synthesis: a factorization approach (Edinburgh, MA: The MIT Press, 1985).Google Scholar
19Wimmer, H. K.. Exponential solutions of systems of linear differential equations of infinite order. J. Differential Equations 33 (1979), 39–44.CrossRefGoogle Scholar
20Wyman, B. F. and Sain, M. K.. A unified pole-zero module for linear transfer functions. Systems Control Letters 5 (1984), 117–120.CrossRefGoogle Scholar