Practical dwell time approach for stability analysis of hybrid systems

The problem of the practical p-th mean stability of a class of stochastic nonlinear and time dependent linear hybrid systems with practically p-mean stable and unstable structures is considered. Sufficient conditions for the practical p-th mean stability under the stabilizing switching signal using Lyapunov techniques, the practical average dwell time and the practical dwell time approach, are derived. Three cases including the existence of the single Lyapunov function, the multiple Lyapunov function and the single practical Lyapunov-like function, for the practical p-th mean stability are discussed. The obtained results are illustrated by an example.