Fault detection filter for linear time varying systems: An algebraic-geometric approach

In this paper we consider the fault isolation problem for the linear time varying systems. Our approach is based on characterization of the observability of LTV systems by Kalman's rank condition, which permits us to design fault detection filters, feeding also the derivatives of the inputs and the outputs. We prove, using a computable method, that the isolation problem can be solved by generalized Luenberger's observer if and only if the detectability and the weak separability of fault signatures holds.