Integrated State/Fault Estimation and Fault-Tolerant Control Design for Switched T–S Fuzzy Systems With Sensor and Actuator Faults

This article proposes an integrated design approach addressing the state/fault estimation (SFE) and fault-tolerant control (FTC) issues for switched T–S fuzzy systems with sensor and actuator faults and external disturbances. A switched fuzzy observer is developed to simultaneously estimate the system states and the sensor and actuator faults from measurement outputs affected by sensor faults. Based on this observer, a switched fuzzy FTC is designed to stabilize the closed-loop system and compensate for the effects of different considered faults, taking into account the presence of external disturbances. The mutual coupling between the estimation unit (SFE) and the control unit (FTC) supports the integrated design of these two units instead of the separated one. However, the separated design is the most adopted in the literature because the integrated design leads to complex stability conditions in the form of bilinear matrix inequalities. This work focuses on the integrated design considering the different interactions between the observer and the controller and thus ensuring good performance in terms of estimation, control, robustness, and fault compensation. For this purpose, a two-step integrated design strategy and a single-step integrated design strategy are proposed to formalize the integrated SFE and FTC design as linear matrix inequalities instead of bilinear ones. These strategies are based on the mode-dependent average dwell time concept, the piecewise Lyapunov function technique, and the robust $H_{\infty }$ approach. The applicability and efficiency of the developed results are illustrated by studying a numerical example and a single-link robotic manipulator.