Abstract
The mathematical theory of discrete-time descriptor systems is different from the theory of normal ones. In spite of some similarities, discrete-time descriptor systems provide radically different behavior such as noncausality. This chapter deals with some important basic aspects of linear discrete-time descriptor systems.
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References
Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer, New York (1989)
Stykel, T.: Analysis and numerical solution of generalized Lyapunov equations. Ph.D. Thesis, Institut fur Mathematik, Techische Universitat, Berlin, Berlin (2002)
Luenberger, D.G., Arbel, A.: Singular dynamic Leontief systems. Econometrica 45, 991–995 (1977)
Lewis, F.L.: Fundamental, reachability, and observability matrices for discrete descriptor systems. IEEE Trans. Automat. Control 30, 502–505 (1985)
Bunse-Genster, A., Byers, R., Mehrmann, V., Nichols, N.K.: Feedback design for regularizing descriptor systems. Linear Algebra Appl. 299, 119–151 (1999)
Kailath, T.: Linear Systems. Prentice-Hall Information and System Sciences Series. Prentice Hall, Englewood Cliffs (1980)
Stewart, G.W., Sum, J.-G.: Matrix Perturbation Theory. Academic Press, New York (1990)
Lancaster, P., Salkauskas, K.: Transform Methods in Applied Mathematics. An Introduction. Canadian Mathematical Society of Monographs and Advanced Texts. Willey, New York (1996)
Lancaster, P., Tismenetsky, M.: The Theory of Matrices, 2nd edn. Academic Press, Orlando (1985)
Doetsch, G.: Guide to the Applications of the Laplace and Z-Transforms. Van Nostrand Reinbold Company, London (1971)
Stykel, T.: Stability and inertia theorems for generalized Lyapunov equations. Linear Algebra Appl. 355(1–3), 297–314 (2002)
Xu, S., Lam, J.: Robust Control and Filtering of Singular Systems. Lecture Notes in Control and Information Sciences. Springer, Berlin (2006)
Gahinet, P., Apkarian, P.: A linear matrix inequality approach to \({\cal{H}_{\infty }}\)-control. Int. J. Robust Nonlinear Control 4, 421–448 (1994)
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Belov, A.A., Andrianova, O.G., Kurdyukov, A.P. (2018). Basics of Discrete-Time Descriptor Systems Theory. In: Control of Discrete-Time Descriptor Systems. Studies in Systems, Decision and Control, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-78479-3_2
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DOI: https://doi.org/10.1007/978-3-319-78479-3_2
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