Domination Design of Robust Adaptive Controller of Nonlinear Time-Delay Systems based on Lyapunov-Razumikhin Function

For general uncertain nonlinear time-delay systems, a domination design approach to robust adaptive controller based on Lyapunov-Razumikhin function is provided. To deal with the obstacle brought by the Lyapunov-Razumikhin function with the Razumikhin condition, a new parameter variable is introduced into the adaptive controller design instead of the conventional parameter variable. Based on Lyapunov-Razumikhin stability theory, it is shown that the proposed robust adaptive controller can guarantee the global uniform ultimate boundedness of all the signals in the resulting closed-loop dynamical system. In addition, it is also shown that the proposed design scheme can be applied to recursive design for the robust adaptive stabilizing controller of general uncertain nonlinear time-delay systems with triangular structure.