Reachability/observability Gramians and balanced realization of periodic descriptor systems

In this talk 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 (GDPLE). 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. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.