Remarks on p-stabilizability of stochastic linear hybrid systems*

Problem of the p-th mean exponential stabilizability of a class of stochastic linear control hybrid systems with unstable subsystems is considered. Sufficient conditions for the p-th mean exponential stabilizability under a feedback control and a stabilizing switching signal, that is constructed based on the Lyapunov techniques, the knowledge of regions of decreasing of Lyapunov functions for subsystems and the average dwell time approach, are derived. Three cases, including the existence of a single Lyapunov function, a multiple Lyapunov function and a single Lyapunov-like function, are discussed. Obtained results are illustrated by an example.