Robust control for incremental quadratic constrained nonlinear time-delay systems subject to actuator saturation

Abstract This article presents a saturation controller design method for a type of nonlinear time-delay systems. Different from the current works, the nonlinear systems considered herein satisfy an incremental quadratic constraint, which is a more general nonlinearity. Firstly, for the constraint in the actuator, the convex set theory is employed to transform the saturated feedback law into a parameterized linear convex hull set. Next, the convex hull Lyapunov function is constructed to obtain sufficient conditions for exponential stability of the closed-loop system. In addition, by solving an optimization problem, the maximal estimation of domain of attraction is also determined. Finally, numerical examples are provided to verify the proposed method.