H_-/H_∞ memory fault detection filtering design for uncertain systems with finite frequency specifications

This article is concerned with the H_-/H_∞ memory fault detection filtering design in finite frequency domain for discrete-time systems with polytopic uncertainties. Under the assumption that both disturbances and faults are restricted to finite frequency ranges, that is, the low, middle, or high frequency range, an admissible memory fault detection filter is developed by using historical information of the system. It is shown that the asymptotic stability with prescribed H_-/H_∞ performance of the closed-loop filtering error system is guaranteed. It is also shown that by using historical system outputs along with parameter-dependent Lyapunov functions, the better performance of the resulting fault detection filter is obtained. With the aid of Projection lemma, sufficient conditions for the fault detection filtering design are established by solving an optimization problem in the form of a set of linear matrix inequalities (LMIs). Finally, three examples are presented to demonstrate the effectiveness and advantages of the proposed approach.