A novel observer method for Markov jump systems with simultaneous sensor and actuator faults*

This work focuses on the fault estimation (FE) problem for Markov Jump Systems (MJS) with sensor and actuator faults, and a novel reduced-order observer-based FE method is proposed. Firstly, an augmented plant in standard form is considered and a new theorem is derived to decouple the augmented fault vectors $d(t)$ from $\bar{x}_{1^{(1)(t)}}$ which is the state vector after the first time coordinate transformation. Then, the novel reduced-order observer is investigated and the Theorem 2 is derived to ensure the asymptotically reconstruction of $x(t)$. Compared with other existing observer-based method for MJS with faults, the advantage is that the FE and state estimation can be obtained directly without any supplementary design. Finally, simulations are provided to demonstrate the effectiveness of the proposed observer approach.