On the Mean Stability of a Class of Switched Linear Systems
نویسندگان
چکیده
This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the Lp-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 p goes to ∞, the stability of the pth 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.
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