Reachability/Observability Gramians and Balanced Realization of Periodic Descriptor Systems

In this paper necessary and sufficient conditions are derived for complete reachability and observability of periodic time-varying descriptor systems. Applying these conditions, the symmetric positive semi-definite reachability/observability Gramians are defined and 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 an illustrative numerical example is given. As an application of our results, the balanced realization of periodic descriptor systems is discussed.