Adaptive fault-tolerant tracking control for Markov jump systems with partly unknown transition probability

This paper studies the adaptive fault-tolerant tracking control problem for a class of continuous-time Markov jump linear systems with partly unknown transition probabilities. The considered transition probabilities are more general, which include completely known case, partly unknown with known lower and upper bounds case and completely unknown case. Firstly, the robust tracking controller for Markov jump system without actuator faults is designed to prepare for the adaptive fault-tolerant control. Then, an adaptive law is presented, which can generate a fault estimation. With the estimated fault parameters, the fault-tolerant controller is constructed to make sure that the output of fault system asymptotically track the reference signal. In the process, the free-connection weighting matrix method is used to deal with the unknown transition probabilities so that the sufficient conditions proposed in this paper are less conservative. Finally, numerical example is given to demonstrate the effectiveness of the proposed method.