Observer-based control for stochastic jump systems via backstepping method

In this paper, an observer-based state feedback control problem is investigated for stochastic jump systems. First, a new approach is developed to design the virtual controller for augmented jump system. Based on backstepping technique and Lyapunov stability theorem, it is shown that an observer for stochastic system can be constructed. Then, a stochastic stability condition is proposed for the overall closed-loop stochastic systems composed of the observer dynamics and the state estimation error dynamics. Finally, A numerical example is given to show the potential of the proposed techniques.