Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays

The robust stabilization method via the dynamic surface control (DSC) is proposed for uncertain nonlinear systems with unknown time delays in parametric strict-feedback form. That is, the DSC technique is extended to state time delay nonlinear systems with linear parametric uncertainties. The proposed control system can overcome not only the problem of "explosion of complexity" inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate Lyapunov-Krasovskii functionals. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded. Finally, an example is provided to illustrate the effectiveness of the proposed control system.