Fault Estimation for Linear Systems with Multi Time-Delay

Abstract

This paper deals with the problem of observer-based fault estimation for a class of linear systems with multi time-delay. The key of this paper is the introduction of a generalized coordinate transform, such that in the new coordinates, all the time-delay terms are injected by the system’s input and output. Based on the new obtained system expression, the design of fault estimator is formulated in the framework of H∞ filtering by incorporating the prior knowledge of fault into the design procedure, and the dynamics of the estimation error is converted into a general linear time invariant form with generalized unknown input time-delay terms. Based on the bounded real lemma, the observer gain matrix is obtained in terms of linear matrix inequality. A numerical example is given to illustrate the effectiveness of the proposed approach.