Robust [formula omitted] observer-based sliding mode control for uncertain Takagi–Sugeno fuzzy descriptor systems with unmeasurable premise variables and time-varying delay

Abstract

This work focuses on the observer-based sliding mode control (OBSMC) synthesis for non-linear T-S fuzzy descriptor time-varying delay systems, which subject to uncertainties and unmeasurable premise variables (UPVs). Due to the state variables are difficult to completely accessible, a sliding mode observer (SMO) is designed to estimate the unmeasurable variables, and the nonlinear systems are represented to an equivalent multiple model (MM) forms under the MM formulation with UPVs. Then two sliding surfaces are proposed for the observer system and error system respectively to ensure stabilization, which can effectively deal with the nonlinearity and uncertainties as well. By the utilization of the linear matrix inequality (LMI) technique, we present the stability criterions such that the sliding mode dynamics with H∞ performance are proved to be admissible. Moreover, the SMC is obtained so we can drive the system trajectories to the predefined sliding surface in a finite time. At last, three simulation examples are provided to certificate the availability of our approach.