Asymptotic and mean square stability conditions for hybrid jump linear systems with performance supervision

This paper addresses the asymptotic and mean square stability of a class of linear stochastic hybrid systems. The systems of interest are composed of a high-level supervisor that drives a closed-loop jump linear system using an external Markovian input and a performance measure of the closed-loop system. Two new testable sufficient conditions for the asymptotic and mean square stability of these so-called hybrid jump linear systems with performance map are introduced. The first condition is also sufficient to determine the asymptotic stability of a deterministic switched system under arbitrary switching. A new testable necessary condition for the asymptotic stability of switched systems is also introduced.