Observer Design for a Class of Time-delay Nonlinear Systems with External Disturbance

This paper is concerned with the problem of  H observer design for a class of time-delay nonlinear systems with external disturbance. The purpose of this problem is to design a  H observers such that, for the addressed nonlinearities as well as all admissible external disturbance in state equation, the observation process remains globally exponentially stable, independently of the time delay. The nonlinearities are assumed to satisfy the global Lipschitz conditions, and the external disturbance are allowed to be time varying, unstructured and norm bounded. An effective linear matrix inequality methodology is developed to solve the proposed problem. We derive the conditions for the existence of the desired robust nonlinear observers, and then characterize the analytical expression of these observers. Numerical examples demonstrate the validity and applicability of the present approach in this paper.