Fault Detection Filtering for Discrete-time Switched Systems with All Subsystems Unstable

In this paper, fault detection (FD) filter design for discrete-time switched system with all subsystems unstable is solved. By designing practical fault detection filters to track the residual signal, we finish the FD. For the existence of unstable subsystem, a proper switching rule is given via average dwell time. In light of the discretized Lyapunov function technology, the exponentially stability is firstly guaranteed. Then, under the stable condition, the $L_{2}-$gain is obtained with the help of matrix augmented technique and linear matrix inequalities (LMIs).In addition, the desired parameters of the FD filters are easily acquired. Eventually, an example is put forward to verify the serviceability.