Robust H∞ sliding mode observer-based fault-tolerant control for One-sided Lipschitz nonlinear systems

This paper presents fault tolerant controllers for a class of one-sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H-infinity filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H-infinity-SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one-sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed-loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.