H_/H∞, Filtering Fault Detection for Asynchronous Switched Discrete-time Linear Systems With Mode-dependent Average Dwell Time

The filtering fault detection problem for asynchronous switched discrete-time linear systems with mode-dependent average dwell time (MDADT) is investigated in this paper. A series of mode-dependent fault detection filters are designed with respect to each subsystem and are equipped with the switched system to obtain an augmented switched system. For the fact that the switching of the filter lags behind that of the subsystem frequently in actual situations, the resulting augmented switched system is consequently converted into an asynchronous augmented switched system. To guarantee the globally uniformly exponentially stability (GUES) and the H_/H-infinity performance of the asynchronous filtering fault detection system, multiple Lyapunov functional and MDADT techniques are then used. The starting instants set of the subsystem is proposed to make it more convenient to apply the MDADT technique. The sufficient conditions for the existence of the designed filter and stability of asynchronous augmented switched systems are given in terms of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed methodology is demonstrated by two examples.