State Estimation and Fault Reconstruction for a Class of Linear Uncertain Time-Delay Systems

This paper is concerned with the problems of robust state estimation and fault reconstruction for a class of time-delay systems with uncertainty. First, a sliding mode observer (SMO) is synthesized to achieve system state estimation. The basic design idea consists of exploiting the SMO concept with an adequate choice of a Lyapunov-Krasovskii functional and the Linear Matrix inequality (LMI) technique. Besides, the developed SMO can force the state estimation error to converge to zero and can drive and maintain this error on the sliding surface in finite time. Thereafter, using the developed SMO and introducing the Bounded Real Lemma (BRL) and the
$H_{\infty}$
concept, a robust actuator fault reconstruction scheme is established. A numerical example is given to illustrate the validity and the applicability of the proposed approaches. At last, a Williams-Otto reactor is introduced to prove the effectiveness of the proposed approaches.