Decay estimates of Green's matrices for discrete-time linear periodic systems

Abstract

We study periodic Lyapunov matrix equations for a general discrete-time linear periodic system , where the matrix coefficients and can be singular. The block coefficients of the inverse operator of the system are referred to as the Green matrices. We derive new decay estimates of the Green matrices in terms of the spectral norms of special solutions to the periodic Lyapunov matrix equations. The study is based on the periodic Schur decomposition of matrices.