An H∞ Disturbance Estimation Approach to Fault Detection for Linear Discrete Time-Varying Systems

Abstract

This paper is concerned with a new fault detection scheme for linear discrete timevarying systems by using an H∞ disturbance estimation approach. A unified estimation problem is formulated for linear discrete time-varying systems in an H∞ framework. Such a formulation not only achieves a novel H∞ disturbance estimation problem but also includes the classical H∞ fault estimation as a special case. By using projection and innovation analysis in the Krein space, the H∞ disturbance and fault estimation problems are solved in a unified way, and their estimates are given in terms of the solution to a set of Riccati difference equations. Then, both the H∞ disturbance and fault estimates are used as residuals for the purpose of fault detection, and the detection performances are discussed based on these two residual generation strategies. It is an interesting finding that, in the case of sensor fault-free, the H∞ fault estimation approach is no longer available while the H∞ disturbance estimation approach is still effective. Finally, a simulation example is employed to illustrate the results derived in this paper.