Simultaneous observation and identification for nonlinear systems under unknown time-varying delays

In this paper, a class of time-delayed nonlinear systems with unknown parameters and unknown time-varying delays is considered. A high gain observer approach is proposed for simultaneous state observation and parameter identification. Sufficient conditions are obtained to ensure the boundedness of both observation and identification errors. Consequently a practical stability of the proposed observer is achieved. Moreover, an exponential stability of the observer is derived from the knowledge of time-delay. Simulation results are given to illustrate the performances of the proposed observer design under time-varying delay function and a piecewise unknown parameter.