Robust Actuator Fault Reconstruction for Uncertain Time-Delay One-Sided Lipschitz Nonlinear Systems Based on a New Sliding Mode Observer

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.