Simultaneous Fault Detection and Control for Continuous-Time Switched Takagi–Sugeno Fuzzy Systems With State Jumps

Abstract

Abstract This article addresses the simultaneous fault detection and control (SFDC) issue for switched Takagi–Sugeno (T–S) fuzzy systems with state jumps. The main objective is to design robust detection filters and observer-based controllers to stabilize this system class and, at the same time, detect the presence of faults. Less conservative stability conditions are developed, applying the mode-dependent average dwell time (MDADT) concept, the robust H∞ approach, and the piecewise Lyapunov function (PLF) technique. Based on these conditions, the integrated controller and detector design is formalized in the form of linear matrix inequalities (LMI) instead of bilinear matrix inequalities (BMI). The proposed LMIs determine the controller/detector gains simultaneously in a single step, thus offering more degrees-of-freedom in the design. Finally, a numerical example and two real systems are studied to prove the applicability and effectiveness of the obtained results.