%0 Journal Article
%T Global Output Control for a Class of Inherently Higher-Order Nonlinear Time-Delay Systems Based on Homogeneous Domination Approach
%A Lin Chai
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/180717
%X This paper addresses the problem of global output feedback stabilization for a class of inherently higher-order uncertain nonlinear systems subject to time-delay. By using the homogeneous domination approach, we 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. In addition, we also show that the proposed approach is applicable for time-delay systems under nontriangular growth conditions. 1. Introduction This paper addresses the global stabilization problem for a class of uncertain systems with delay which is described by where are the system states, is the control input, is the system output with , is a given time-delay constant, and is the initial function of the system state vector. The terms , , represent nonlinear perturbations that are not guaranteed to be precisely known. It has been known that the problem of global output feedback stabilization for uncertain nonlinear systems is very challenging compared to the state feedback case. In the past decade, global stabilization by output feedback domination method has been proved to be achievable for a series of nonlinear systems. For the system of a five-spot pattern reservoir, a nonlinear reduced-order model is identified and an asymptotically stabilizing controller is proposed based on the circle criterion in [1]. With the help of linear feedback domination design [2], some interesting results have been established under a linear growth condition [2] and under a higher-order growth condition [3]. Recently, the homogeneous domination approach proposed in [3] has been used as a universal tool to solve the problem of global output feedback stabilization for inherently nonlinear systems. As a consequence, fruitful research results have been achieved in [3¨C9]. However, the aforementioned results have not considered the time-delay effect which is actually very common in state, input, and output due to the time consumed in sensing, information transmitting, and controller computing. In the case when the nonlinearities contain time-delay, some interesting results have been obtained. For instance, in [10], the global asymptotic stability analysis problem is investigated for a class of stochastic bidirectional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The paper [11] investigated the state
%U http://www.hindawi.com/journals/ddns/2013/180717/