Robust sensor fault reconstruction of uncertain time-delay systems using an extended Sliding Mode Observer

In this paper, we propose a robust sensor fault reconstruction method for a class of linear uncertain delayed systems using an extended Sliding Mode Observer (SMO). The uncertainty considered is matched and bounded. In meantime, the time-varying delay is unknown, bounded and affects simultaneously the input and the state of the system. Using the H_∞ concept and applying the equivalent output error injection idea from previous works in Fault Detection and Isolation (FDI) scheme, the estimate sensor fault signal is designed with the proposed observer that minimizes the uncertainty and the time-varying delay effects. Therefore, this problem is solved via Linear Matrix Inequalities (LMIs) optimization. A numerical example is given to illustrate the validity and the applicability of the proposed approach.