Sensor Fault Estimation and Fault-Tolerant Control for a Class of Takagi-Sugeno Markovian Jump Systems with Partially Unknown Transition Rates Based on the Reduced-Order Observer

This paper addresses the problem on sensor fault estimation and fault-tolerant control for a class of Takagi-Sugeno Markovian jump systems, which are subjected to sensor faults and partially unknown transition rates. First, the original plant is extended to a descriptor system, where the original states and the sensor faults are assembled into the new state vector. Then, a novel reducedorder observer is designed for the extended system to simultaneously estimate the immeasurable states and sensor faults. Second, by using the estimated states obtained from the designed observer, a statefeedback fault-tolerant control strategy is developed to make the resulting closed-loop control system stochastically stable. Based on linear matrix inequality technique, algorithms are presented to compute the observer gains and control gains. The effectiveness of the proposed observer and controller are validated by a numerical example and a compared study, respectively, and the simulation results reveal that the proposed method can successfully estimate the sensor faults and guarantee the stochastic stability of the resulting closed-loop system.