Abstract
This article presents the problem of non-linear observer design for a class of time-delay non-linear systems with uncertainty. The non-linearity 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 the non-linear terms satisfy the Lipschitz condition. A discontinuous observer for the system in the presence of a time-dependent uncertainty, based upon the sliding mode techniques, is designed to yield a feedforward compensation input to stabilise 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 non-linear observer for systems with uncertainties.