Sliding mode state observation for nonlinear systems

In this paper a class of non-linear systems with uncertainty and a Lipschitz part is considered. The non-linear part satisfies the Lipschitz condition, whilst the uncertain part is a bounded function. A sliding mode observer is designed to yield feedforward compensation input to stabilize the error estimation system with and without a Lipschitz non-linearity. Sufficient conditions for stability of the Thau observer are also proposed. These conditions ensure the stability of the non-linear observer by selecting a suitable observer gain matrix. In general, when the system contains unmatched uncertainty, ultimate boundedness is obtained. The ultimate boundedness radius depends upon the defined 'distance of the unmatched uncertainty'. Some sufficient conditions may ensure the stability of a non-linear observer for systems with uncertainties.