Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

The paper addresses the fault detection (FD) problem for a class of discrete-time Markov jump linear systems (MJLSs) with deficient transition rates, which simultaneously considers the totally known, partly unknown, and uncertain transition rates. Then, in accordance with the linear matrix inequality (LMI) method and the convexification techniques, a sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained, which can ensure the error augmented system with the FD reduced-order filter is stochastically stable. In addition, a performance index is given to enhance the robustness of the residual system against deficient transition information and external disturbance, such that the error between the fault and the residual is made as small as possible to reinforce the faults sensitivity. Finally, an illustrative example is employed to show the effectiveness of the proposed design approach.