On the stability of discrete-time linear switched systems in block companion form

Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work we study the arbitrary switching stability for some classes of discrete-time switched systems whose dynamic matrices are in block companion form. We start from the special family of block companion matrices whose Þrst block-row is made of permutations of nonnegative matrices, deriving a simple necessary and sufficient condition for its arbitrary switching stability. Then we relax both these assumptions, at the expense of introducing some conservatism. Some consequences on the computation of the Joint Spectral Radius for the aforementioned families of matrices are illustrated.