Stabilization of hybrid stochastic systems in the presence of asynchronous switching and input delay

Abstract

Abstract This paper studies the p th moment and almost sure stabilization of a class of nonlinear hybrid stochastic systems with input delays in both the switching signal and the state. By using Lyapunov functional approach, sufficient conditions are established in terms of sizes of the delays ensuring the p th moment exponential stability of the systems. By developing a composite mode-dependent Lyapunov function approach, we derive novel almost sure exponential stability criteria for a delay-free hybrid stochastic system without imposing the stability condition on the subsystems. We further prove that the almost sure stability property of the hybrid system with delayed feedback controller is preserved as long as the corresponding delay-free system is almost sure exponential stabilization and the delays are small enough. Numerical examples demonstrate the theoretical results.