Backstepping Control for Nonlinear Time-Delay System via L-K Function

Abstract

The state feedback control problem is addressed for a class of nonlinear time-delay systems. The time delays appear in all state variables of the nonlinear system, which brings a challenging issue for controller design. With an introduced new Lyapunov–Krasovskii functional and the help of backstepping method, we develop memoryless state feedback controller, which does not need the precise knowledge of time delay. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delay. We apply the developed method to the control design of a two-stage chemical reactor with delayed recycle streams, and the simulation results verify the effectiveness of the main results.