Adaptive stabilization for a class of uncertain high-order time-delay nonlinear systems

This paper is concerned with adaptive stabilization for a class of uncertain high-order time-delay nonlinear systems. To the authors´ knowledge, there has been no analogous result, and hence during investigation, the conditions on delay effect and the control design framework should be established for the first time. In this paper, under somewhat necessary restrictions on the system nonlinearities, by the method of adding a power integrator and the related adaptive technique, a design procedure is successfully developed to the continuous adaptive state-feedback controller without overparametrization. Moreover, the uniform stability and convergence of the resulting closed-loop system are rigorously proven, with the aid of an suitable Lyapunov-Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical result.