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On the mean stability of a class of switched linear systems
This paper investigates the mean stability of a class of discrete-time
stochastic switched linear systems using the -norm joint spectral radius
of the probability distributions governing the switched systems. First we prove
a converse Lyapunov theorem that shows the equivalence between the mean
stability and the existence of a homogeneous Lyapunov function. Then we show
that, when goes to , the stability of the th mean becomes
equivalent to the absolute asymptotic stability of an associated deterministic
switched system. Finally we study the mean stability of Markovian switched
systems. Numerical examples are presented to illustrate the results