Based on UIO fault estimation for Markov jump systems

A robust fault estimation (FE) method is proposed for Lipschitz nonlinear Markov jump system (MJS) based on unknown input observer (UIO). Firstly, the robust UIO is designed under the unknown input and output noise. Then the state estimation error system is established by combining the observer estimated states with real system states. When the error system is stable, the system states and the actuator faults can be estimated simultaneously. Compared with previous studies, the unknown input is not assumed to be decoupled completely and the noise is existed in the output. To solve these cases, the robust H_∞ optimization method is used. A sufficient stability condition of the error system is derived by applying linear matrix inequality (LMI) technique, and the observer gain also can be obtained by solving a set of LMIs. A numerical example shows the effectiveness of the proposed method.