Stabilisation of nonlinear hybrid stochastic systems with time-varying delay by discrete-time feedback controls with a time delay

Abstract

In this paper, we investigate stabilisation of hybrid stochastic systems with time-varying delay by feedback control based on discrete-time state and mode observations with a time delay. By constructing a proper Lyapunov functional, the , asymptotic and exponential stability of the controlled systems are studied in the pth moment sense for p>1. Meanwhile, we obtain the upper bound on the duration τ between two consecutive state and mode observations. At last, two numerical examples are illustrated to support our theoretical results.