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.

This paper is concerned with the problems of sliding mode observer (SMO) design and robust fault reconstruction for one-sided Lipschitz (OSL) nonlinear systems with uncertainty and time-delay. Bounded uncertainty and varying time-delay are considered. First, the linear matrix inequality (LMI) optimization and a Lyapunov-Krasovskii functional are exploited to obtain a new observer. A sufficient condition is given such that the reachability condition can be ensured. Then, using the new SMO and by selecting an appropriate Lyapunov-Krasovskii functional, the$H_{\infty}$concept and a bounded real lemma (BRL), a robust actuator fault reconstruction is achieved. At last, a single-link flexible joint robotic system is included to illustrate the validity and the applicability of the proposed approaches.