Asymptotic Stabilization of Time-Varying Delay System with Actuator Saturation via Multi-dimensional Taylor Network

This paper addresses the stabilization problem of time-varying delay systems subject to actuator saturation. A novel class of Lyapunov functional with a nonlinear metric is developed to guarantee that there exists a Lyapunov-Razumikhin function that strictly decreases for the controlled system. Such a nonlinear metric is parameterized by a multi-dimensional Taylor network with concise topology, which brings into the high-order dynamic information and guarantees real-time performance. A sum-of-squares programming approach based on the designed Lyapunov functional is formulated to deduce the stability criteria, which maximizes the estimate of the region of attraction and ensures the uniform asymptotic stability of the closed-loop system theoretically. A numerical example demonstrates the effectiveness of the proposed stabilization control scheme.