Abstract
Switched models whose dynamic matrices are in block companion form arise in theoretical and applicative problems such as representing switched ARX models in state-space form for control purposes. Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work, the authors study the arbitrary switching stability for some classes of block companion discrete-time switched systems. They start from the special case in which the first block-row is made of permutations of non-negative matrices, deriving a simple necessary and sufficient stability condition under arbitrary switching. The condition is computationally less demanding than the sufficient-only existence of a linear common Lyapunov function. Then, both non-negativity and combinatorial assumptions are dropped, at the expense of introducing conservatism. Some implications on the computation of the joint spectral radius for the aforementioned families of matrices are illustrated.
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