Linear and nonlinear stabilizing continuous controllers uncertain dynamical systems including state delay

The problem of robust stabilization of a class of time-varying dynamical systems with disturbance, uncertain parameters, and a bounded time-varying state delay is considered. Two classes of stabilizing continuous controllers are proposed. The proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems. Moreover, since the proposed controllers are completely independent of the time delay (which is only assumed to be any nonnegative bounded and continuous function), the results developed in this note are applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.