Global state feedback stabilization of high-order nonlinear systems with multiple time-varying delays

Abstract

This paper studies the global stabilization problem for a class of high-order nonlinear systems with low-order and high-order nonlinearities, and multiple time-varying delays. Systems become more general due to both low-order and high-order in nonlinearities taking values in certain intervals. By introducing a novel Lyapunov–Krasovskii functional, a state feedback controller based on the Lyapunov–Krasviskii theorem together with the adding a power integrator and sign function methods is designed to guarantee the globally uniformly asymptotic stability of the closed-loop system.