Sliding Mode Observer for Uncertain Nonlinear Systems based on Generalized Lipschitz Condition

In this paper, a sliding mode observer for the class of Lipschitz nonlinear systems with uncertainty is proposed. The uncertainty is assumed to be bounded and the matching condition is first taken into account. The generalized Lipschitz condition is employed to consider some structural knowledge of Lipschitz nonlinearity. This yields less conservative results in stability analysis of proposed observer dynamics. The results are then extended to the unmatched uncertainty. Moreover, a synthesis method in terms of some linear matrix inequalities is established to achieve the proposed sliding mode observer. The simulation results on manipulator with revolute joints actuator are finally given to exhibit the effectiveness of the proposed observer and related synthesis method.