Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay

Abstract

This paper focuses on the problem of robust H∞ sliding mode observer (SMO) design for a class of Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delay. A SMO is designed by taking the control input and the measured output into account. Then a novel integral-type sliding surface, which involves the SMO gain matrix, is constructed for the error system. By using an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamic to be robustly admissible with H∞ performance and determines the SMO gain matrix. Moreover, a sliding mode control (SMC) law is synthesized such that the reachability can be ensured. Finally, simulations are presented to show the effectiveness of our results.