Observer design for a class of nonlinear time-delay systems

This paper is devoted to design of observer for a class of Lipschitz nonlinear state delay systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, in which linear matrix inequalities (LMIs) are solved. When certain LMIs are satisfied, the explicit expression of a desired nonlinear observer is presented. A numerical example and the simulating results are provided to demonstrate the applicability of the proposed approach.