Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems

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, we develop a novel control strategy. With the help of a backstepping method, we design a memoryless state feedback controller, which does not need the precise knowledge of time delays. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delays. 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.