Sliding mode control for Markovian jump systems with external disturbance

In this paper, the adaptive sliding mode control problem of nonlinear Markovian jump systems (MJSs) is studied. Our attention is mainly focused on designing an adaptive sliding mode controller for such a complex dynamics. Firstly, for each mode, we construct appropriate mode-dependent sliding mode surface, of which the stochastic stability is guaranteed by some sufficient conditions. Secondly, an adaptive sliding mode controller is designed such that the MJSs state trajectories satisfy the reaching condition. Then, the stochastic stability of the closed-loop system can be guaranteed. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed scheme.