Boundary control of delayed ODE-heat cascade under actuator saturation

In this paper, we consider boundary stabilization for a cascade of ODE-heat system with a time-varying state delay under actuator saturation. To stabilize the system, we design a state feedback controller via the backstepping method and find a bound on the domain of attraction. The latter bound is based on Lyapunov method, whereas the exponential stability conditions for the delayed cascaded system are derived by using Halanay's inequality. Numerical examples illustrate the efficiency of the method.