Observer-based sensor fault-tolerant control for semi-Markovian jump systems

This paper investigates the state estimation and fault-tolerant control problems for a class of semi-Markovian jump systems with external disturbance and sensor fault. In this study, the original system is decomposed into two subsystems, where disturbance only exhibits in the first subsystem, and sensor fault only exists in the second subsystem. Two new observers are designed to eliminate the effects of fault and disturbance, respectively. Then, an observer-based sliding mode control scheme is proposed to stabilize the fault closed-loop system and the reachability of the proposed sliding mode surface can be guaranteed. By transforming the time-varying transition rate into convexification of the polytopic-type form, sufficient conditions for the existence of the gain of the observer and controller are obtained through solving a set of linear matrix inequalities. Finally, two numerical examples where the first one contains three modes and the second one is the linearized model of an F-404 aircraft engine system, are presented to illustrate the effectiveness of the proposed control method.