Fault detection for delay-switched systems with all subsystems unstable

The fault detection problem of a class of linear discrete switched systems with time delay is studied, where the subsystems of the systems are all unstable. The main idea of this article is to design a fault detection filter to turn the detection problem into a H∞ filter problem. In this paper, we use a special dwell time and Lyapunov function, introduce the weighted fault matrix, and the sufficient conditions for the stability of the augmented systems are obtained by using the linear matrix inequality method. Finally, an example is used to verify the effectiveness of the fault detection filter designed in this paper.