Adaptive Global Stability of Nonlinear Pure-Feedback Systems With Unknown Time-Varying Delays

This paper investigates the backstepping control problem for nonlinear pure-feedback systems with time-varying delays. A virtual controller is designed to counteract the effects caused by the state perturbation of time delay, and improve the stability of the system. The assumption on delay-dependent nonlinearities is further relaxed by a backstepping auxiliary controller and a Lyapunov–Krasovskii functional. A suitable coordinate transformation is introduced to reduce the complexity of computation caused by nonaffine structures. The globally uniform boundedness of the closed-loop signals and the asymptotical stability of the state are proved by Lyapunov–Krasovskii stability theory. Finally, the effectiveness of our method is demonstrated by two illustrations.