Lower Triangular Factor-Based Fault Estimation and Fault-Tolerant Control for Descriptor Markovian Jump Systems with Multiple Faults

This paper considers the observer-based fault estimation and fault-tolerant control for descriptor Markovian jump systems (DMJSs). The goal of this paper is to estimate the actuator faults, sensor faults, and the state simultaneously, and then design a controller based on the estimation to stabilize the DMJS. Firstly, the state, actuator faults, and sensor faults are extended to new state variables to obtain an augmented system. Then, a lower triangular factor-based estimation observer (LTFEO) is proposed to estimate the state and multiple faults and to eliminate the influence of sensor faults. It is proved that the descriptor error system is derivative input-to-state stable (DISS) with respect to the derivative of the faults. Furthermore, based on the fault estimation, a fault-tolerant control scheme is proposed to guarantee the overall closed-loop system DISS. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme and control strategy