Integral sliding mode control for stochastic Markovian jump system with time-varying delay

The mean-square exponential stabilization problem of stochastic Markovian jump system subject to time-varying delays and uncertainties has been investigated by using integral sliding mode control technique. Firstly, in order that the system trajectories can be kept on the integral sliding surface almost surely since the initial time, an integral sliding surface is constructed by properly choosing some matrices. On this basis, a novel sliding mode controller is designed to guarantee that the states will be kept on the sliding surface. Then, the sufficient condition in terms of linear matrix inequalities is presented to ensure that the mean-square exponential stability of the states can be guaranteed. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.