Robust Sliding-Mode Control for Fuzzy Stochastic Singular Systems With Different Local Input Matrices

Abstract

In this paper, the stabilization is investigated about fuzzy stochastic singular systems by the use of sliding-mode control (SMC). The advantage of this paper is that local input matrices of fuzzy systems could be different, and the SMC law provided in this paper still has strong robustness to resist external disturbance. In order to deal with the problem of different input matrices, a novel sliding-mode surface is proposed which consists of some sub-surfaces, but not all the considered systems can reach the sliding-mode surface. Hence, a lemma is given to judge what kind of systems can be stabilized. In order to deal with stochastic problem, by the use of an improved technique different from the traditional Lyapunov method, a novel SMC law is designed to make the system reach the designed sliding-mode surface and keep on it thereafter. The other advantage is that the matrices $\overline {E}_{i}$ describing sub-singular systems could be different. In this paper, by the use of a lemma, different matrices $\overline {E}_{i}$ could be changed into an identical one. Finally, two examples are provided to verify the validity of the method proposed in this paper.