Robust Stabilization of Parametric Strict-Feedback Nonlinear Systems with Unknown Time Delays: Dynamic Surface Design Approach

The dynamic surface control (DSC) method is proposed for uncertain nonlinear systems with unknown time delays in parametric strict-feedback form. That is, the DSC technique is extended to time delay nonlinear systems with linear parametric uncertainties. Thus, the proposed control system can eliminate the problem of "explosion of complexity" inherent in the backstepping design method. Also, by choosing appropriate Lyapunov-Krasovskii functionals, the uncertainties of the unknown time delays can be compensated. In addition, we prove that all the signals in the closed-loop system are semi-globally uniformly bounded. Finally, an example is provided to illustrate the effectiveness of the proposed control system