Robust hybrid control for nonlinear stochastic markovian switching systems with time delay

This paper deals with the problem of robust hybrid control combining state feedback control with impulsive control for nonlinear stochastic Markovian switching systems (SMSS) with time delay. Firstly, by Lyapunov and linear matrix inequalities (LMIs) approaches, a novel delay-dependent criterion of impulsive control is given. Under the appropriate pure impulsive control, the system under study is stochastically stable in mean square. Then under impulsive control, the state feedback control problem for the system is investigates and the desired state feedback controller is designed. The introduced hybrid controller ensures robustly stochastically stable in mean square of the resulting closed-loop system for all admissible uncertainties and time delay.