Global stabilization via homogeneous output feedback for a class of uncertain nonlinear systems subject to time delays

Abstract

This paper addresses the problem of global output feedback stabilization for a class of uncertain nonlinear systems subject to time delay. Using the homogeneous domination approach, we first construct a homogeneous output feedback controller with an adjustable scaling gain. With the aid of a homogeneous Lyapunov–Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the closed-loop system globally asymptotically stable. As a special case, a linear output feedback controller with a tunable scaling gain is constructed to globally stabilize time-delay systems under a linear growth condition. In addition, we also show the proposed approach is applicable to the time-delay systems under lower-order growth conditions and non-triangular growth conditions.