Robust fault detection filter design for uncertain linear discrete time-varying systems

In this paper, we study the fault detection filter (FDF) design problem for linear discrete time-varying (LDTV) systems with model uncertainties and norm bounded unknown inputs. An alternative indefinite quadratic performance criterion is introduced in lieu of the standard H_∞ performance, and the design issue is converted to an optimization problem of finding the positive minimum of the new defined criterion under a fixed condition. By introducing a corresponding state-space model in Krein space, the projection technique is used to solve the reformulated optimization problem. A recursive algorithm and an explicit condition for the existence of this FDF are obtained. An example is given to demonstrate the effectiveness of the proposed method.