On Stochastic ISS of Time-Varying Switched Systems With Generic Lévy Switching Signals

Switched systems in which switching among subsystems occurs at random time instants find numerous applications in engineering. Stability analysis of such systems, however, is quite challenging. This letter investigates the stochastic input-to-state stability of this class of switched systems. The random switching instants are modeled by a non-decreasing, positive, and real-valued Lévy process, which, at every time instant, selects the active subsystem from a family of deterministic systems. No assumption on the stability of subsystems is presumed; they can be stable or unstable. Stochastic properties of the switching signal are coupled with a family of Lyapunov-like functions to obtain a sufficient condition for stochastic input-to-state stability.