Design of Fault Observer for Linear Discrete Switched Systems

In order to solve the problems of faults and disturbances in linear switched systems, a new fault observer design method is proposed by combining robust observer design with the zonotpoes technology. First, the system fault is regarded as an augmented state, and an augmented system equivalent to the original system is constructed. With the switching signal satisfying the constraint of mean dwell time, the multi Lyapunov function method is used to make the switching system globally exponentially stable and meet the weighted $H_{\infty}$ performance index. Then, the zonotpoes technique is introduced into the interval estimation method, and the state estimation error at each time is recursively obtained by using the center and boundary generation matrix, so that the fault interval can be more accurately shrunk. Finally, a numerical example is given to demonstrate the proposed theoretical result.