Sliding Mode L2-L Infinity Control for Uncertain Stochastic Nonlinear Jump Systems

The problems of stochastic stability and sliding mode L₂-L_infin control for a class of nonlinear matched and mismatched uncertain systems with stochastic jumps are considered in this paper. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix. The transition of the jumping parameters in the systems is governed by a finite-state markov process. A sufficient condition is given for the existence of integral sliding surface in terms of linear matrix inequalities (LMIs). Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. Moreover, a state feedback robust L₂-L_infin controller is also constructed by using the solution of LMIS. Finally, we give a design example in order to show the effectiveness of our method.