Nonlinear observers for a class of continuous-time uncertain state delayed systems

This paper is concerned with the problem of observer design for a class of time-delay nonlinear systems with parameter uncertainties. The purpose of this problem is to design the gain-scheduled state observers such that, for the addressed nonlinearities as well as all admissible parameter uncertainties in state and output equations, the observation process remains globally exponentially stable, independently of the time delay. The nonlinearities are assumed to satisfy the global L ipschitz conditions, and the parameter uncertainties are allowed to be time varying, unstructured and norm bounded. An effective matrix inequality methodology is developed to solve the proposed problem. W e derive the conditions for the existence of the desired robust nonlinear observers, and then characterize the analytical expression of these observers. Two numerical examples demonstrate the validity and applicability of the present approach.