Delayed stabilization of Korteweg–de Vries–Burgers equation by constrained control

This paper addresses non-local control design of 1-D nonlinear Korteweg–de Vries–Burgers equation in the presence of variable input delay, actuator saturation as well as sampled-data switching control. By using the modal decomposition approach, we divide the original system into N+1 unstable modes and infinitely many stable modes. Based on the N+1 unstable modes, we design a finite-dimensional controller to stabilize the system. The well-posedness of the closed-loop system is established by semigroup theory and the step method. To prove regional H¹-stability of the closed-loop system, we construct an appropriate Lyapunov–Krasovskii functional and derive sufficient conditions for stability. An estimate is provided for the set of initial conditions starting from which the state trajectories of the system are exponentially converging to origin. Switched controller is designed based on the sampled-data state-depend switching law. Numerical example illustrates the efficiency of the method.