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Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems. (English) Zbl 1140.93418

Summary: From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.

MSC:

93C55 Discrete-time control/observation systems
15A24 Matrix equations and identities
93B05 Controllability
93B07 Observability
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