Adaptive robust controller design of uncertain nonlinear time-delay dynamical systems

The problem of adaptive robust stabilization is considered for a class of uncertain nonlinear dynamical systems with multiple nonlinear delayed state perturbations and external disturbances. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, it is not required that the nonlinear terms including delayed states are linear norm-bounded in the states. In particular, it is not assumed that the uncertaities and external disturbances have to satisfy the matching conditions. A class of continuous memoryless adaptive robust state feedback controllers is synthesized for such uncertain nonlinear time-delay systems. The standard adaptive backstepping design approach is properly modified to allow the use of our adaptive robust control technique for uncertain nonlinear time-delay dynamical systems. By making use of Lyapunov-Krasovskii functional method, it is also shown that the proposed memoryless adaptive robust control schemes can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems.