Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solution are firstly presented by using the inequality of mathematic expectation of Lyapunov function and its infinitesimal generator. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique asymptotically stable solution. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique asymptotically stable solution in unbiased case and has a unique bounded-in-probability solution in biased case.