An innovations approach to fault diagnosis in linear time-varying descriptor systems

In this paper fault diagnosis is studied for linear time varying descriptor systems, the discrete time counter-part of dynamic systems described by differential-algebraic equations. The Kalman filter for descriptor systems is first revisited by completing existing results about its properties that are essential for the purpose of fault diagnosis. Based on the analysis of the effects of the considered actuator and sensor faults on the innovation of the Kalman filter, it is shown that the considered fault diagnosis problem in linear time varying descriptor systems is equivalent to a classical linear regression problem formulated by appropriately filtering the input-output data. Following this result, algorithms for fault diagnosis through maximum likelihood estimation are then proposed. A numerical example is presented to illustrate the proposed method.