T-S fuzzy observer and actuator fault-tolerant controller designs for descriptor systems

This work focuses on designing an observer to measure states and actuator faults as well as fault-tolerant control (FTC) for fuzzy Takagi-Sugeno (T-S) singular systems. An enhanced system is built by creating a new vector from the system state and the actuator faults. The first task is simultaneously to estimate system states and actuator faults with an adaptive observer. Then, in order to get a stabilized faulty singular system, we conceive an observer based on FTC. Using Lyapunov's approach, a linear matrix inequalities (LMIs) feasibility problem is formulated to provide the controller and the observer gains. Compared with previous studies, the proposed method significantly simplifies the design and simultaneously provides the controller and the observer gains in one step. Finally, three examples are given to demonstrate the effectiveness of the proposed control.