A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems

This paper considers the problem of prescribed-time control for a class of nonlinear uncertain time-delay systems. First, the definition of prescribed-time stability for nonlinear time-delay systems is given, and the necessary conditions to realize the finite-time (including fixed/prescribed-time) stabilization of the nonlinear time-delay system are illustrated. Then, the prescribed-time Lyapunov stability theorem is proposed by utilizing the prescribed-time adjustment function and Lyapunov–Krasovskii (L–K) functional method. The stability of the resulting closed-loop system is proved and the different situations for uncertain time-delay systems are discussed. For first-order fully actuated system, a continuous controller is designed. The effects of different prescribed-time adjustment functions on the controller are also studied. Finally, a simulation example is provided to show the effectiveness of the theoretical results.