Fault detection for switched systems with finite-frequency specifications

This paper is concerned with the fault detection filter design problem for a class of discrete-time switched systems whose output can track a time-varying and known frequency region reference input under arbitrary switchings. Faults detection filters are designed to guarantee that the disturbance attenuation performance is satisfied for all subsystems, the reference input attenuation performance is satisfied for the fault-free case, meanwhile, the reference input sensitivity performance is satisfied for the fault cases. With the aid of virtue of the frequency of the reference input in the finite-frequency region which is known beforehand, the finite-frequency H (-) performance for switched systems is firstly defined. Sufficient conditions for the fault detection filter are given in terms of solutions to a set of linear matrix inequalities, furthermore, the filter gains are characterized in terms of the solution of a convex optimization problem. A numerical example is used to demonstrate the effectiveness of the proposed design method