Finite-Frequency Fault Detection Filter Design for Discrete-Time Switched Systems

In this paper, the finite-frequency fault detection filter design for discrete-time switched systems is investigated. The frequencies of the faults and the unknown disturbance input are assumed to be finite and in three known intervals, qualified as low-, middle-, and high-frequency intervals. Based on the switched Lyapunov function and the generalized Kalman-Yakubovic-Popov lemma, efficient conditions are obtained to guarantee the existence of a finite-frequency fault detection filter, such that the error system is asymptotically stable with an H_{\infty }/H_{-} performance index. Finally, a chemical reactor control system is employed to illustrate the obtained techniques.