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 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 NW are obtained. An example is given to demonstrate the effectiveness of the proposed method.