Abstract
A polynomial matrix G(z )= Iz m −∑ m−1 i=0 Ciz i with complex coefficients is called discrete-time stable if its characteristic values (i.e. the zeros of detG(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.
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