Discontinuous observers for non-linear time-delay systems

This paper presents the problem of nonlinear observer design for a class of time-delay nonlinear systems with uncertainty. The nonlinearity of this class of systems has to satisfy the Lipschitz condition whilst the uncertain term is a bounded function. Various performance indices are analysed to test the stability of the error system when all nonlinear terms satisfying the Lipschitz condition. A discontinuous observer for the system in the presence of a timedependent uncertainty based upon the sliding mode techniques is designed to yield feedforward compensation input to stabilize the error estimation system. The delays are not constant but they are bounded with bounded derivatives. A sufficient condition is required to ensure the stability of a nonlinear observer for systems with uncertainties.