Block companion matrices, discrete-time block diagonal stability and polynomial matrices

Abstract

A polynomial matrix G(z) = Iz m -∑ m-1 i=0 C i z i with complex coefficients is called discrete-time stable if its characteristic values (i.e. the zeros of det G(z) ) are in the unit disc.A corresponding block companion matrix C is used to study discrete-time stability of G(z) .The main tool is the construction of block diagonal solutions P of a discrete-time Lyapunov inequality P -C * PC 0 .