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Ansgar Rehm, Frank Allgöwer

H_∞ Control of Discrete-Time Descriptor Systems

This paper presents a theoretical contribution to H_∞-control of linear discrete-time descriptor systems. The problem under consideration is to causally stabilize a discrete-time descriptor system by means of static feedback of the descriptor vector such that the resulting closed loop system is H_∞ norm-bounded. The presented approach is based on a linear matrix inequality (LMI) characterization of causal, stable, and H_∞ norm-bounded discrete-time descriptor systems. The occuring matrix variable is closely related to the Lyapunov function of the given descriptor system. Application of this result to the control problem renders nonlinear matrix inequalities which additionally to the Lyapunov-type matrix include the feedback matrix as variable. In the paper at hand a procedure is developed that relates this nonlinear matrix inequalities to LMIs and thus allows to access the problem by feasible numerical methods.

at – Automatisierungstechnik, Oldenbourg Wissenschaftsverlag

Print ISSN: 0178-2312
Volume: 52, 09/2004
Pages: 440 - 445

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