Adaptive observer for a class of nonlinear time delay systems

In this paper, one proposes adaptive observers for a class of uniformly observable nonlinear systems with general nonlinear parameterizations and in the presence of one (or more) variable and known delay(s). The proposed approach consists of a systematic procedure for the high gain observers where the state and the unknown parameters of the considered systems are supposed to lie in bounded domains whose size can be arbitrarily large. The exponential convergence of the observer relies on the resolution of an algebraic Lyapunov equation and leads to an explicit expression of the observer gain. The performances of the proposed observer are evaluated through a numerical example at the end of the paper.