Cascade integral observer based feedback linearization of nonlinear time-delay systems

It is well known that traditional high gain observers face peaking problem during the transient period, this undesirable properties could cause more serious degradation if the systems is attached with time delay. This paper solves this problem by constructing a cascade integral observer to estimate the future states of time-delay systems. With a distinctive structure, the predictive observer, which is also called predictor, can handle time-varying delays and eliminate the "peaking phenomenon" during the transient period. Then, a predictor-based output feedback control is designed to guarantee the boundedness of system states. Lyapunov-Krasovskii functional and perturbation theories are used to prove the convergence of the estimation error and the closed-loop system. Finally, a numerical example illustrates the effectiveness of the proposed methodology.