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.


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