Robust adaptive control schemes for a class of uncertain dynamical systems with multiple time delays

The problem of robust adaptive control for a class of uncertain dynamical systems with multiple time delays is considered. Both of the parameters of the systems to be controlled and the upper bounds of the system uncertainties are assumed to be unknown. A scheme of direct adaptive control for this class of uncertain time-delay dynamical systems is proposed. A class of Lyapunov-Krasovskii functionals is constructed, and based on Lyapunov theory, it is shown that the uncertain closed-loop time-delay dynamical system resulting from the proposed adaptive control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results.