Fault Estimation for Linear Systems with Multi Time-Delay

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 Hoc, 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.