Design of adaptive sliding mode observers for nonlinear systems with mismatched perturbations

Based on the Lyapunov stability theorem, a sliding mode observer is proposed in this paper for a class of single-input uncertain nonlinear systems with mismatched perturbations. Firstly the proposed observer with adaptive mechanisms embedded is presented so that the upper bounds of perturbations are not required to be known in advance, and the first state estimation error is able to reach zero within a finite time. Secondly stability analysis is demonstrated to ensure that not only the perturbations are suppressed effectively but also the rest of state estimation errors are capable of achieving asymptotic stability. A numerical example is illustrated for showing the feasibility of the proposed methodology.