Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems. A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input. An adaptive asymptotically stabilizing controller, which can guarantee the stability of the closed-loop system and the convergence of the original system state, is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) and nonlinear adaptive techniques. Some numerical examples are presented to demonstrate the effectiveness of the derived controller.