Fault-Tolerant Control for T-S Fuzzy Stochastic Singular Systems

Abstract

This article investigates the problem of fault estimation and fault-tolerant control for a class of Takagi–Sugeno fuzzy stochastic singular systems. An integral-type sliding-surface-based augmented singular sliding-mode observer, which is applicable to both dual-normalized and nondual-normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then, a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated, and the open-loop system can be stabilized. Moreover, a new adaptive sliding-mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.