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Title: Delay-Independent Asymptotic Stability in Monotone Systems
Authors: Devane, Eoin 
Lestas, Ioannis 
Keywords: Asymptotic stability;Time-delay;Monotone systems;Nonlinear systems
Category: Electrical Engineering - Electronic Engineering - Information Engineering
Field: Engineering and Technology
Issue Date: 1-Sep-2016
Publisher: Institute of Electrical and Electronics Engineers Inc.
Source: IEEE Transactions on Automatic Control, 2016, vol. 61, no. 9, Article no. 7321008, pp. 2625-2631
DOI: 10.1109/TAC.2015.2498137
Journal: IEEE Transactions on Automatic Control 
Abstract: Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity time-delayed systems become monotone, and some remarkable properties have been reported for such systems. These include, for example, the fact that for linear systems global asymptotic stability of the undelayed system implies global asymptotic stability for the delayed system under arbitrary bounded delays. Nevertheless, extensions to nonlinear systems have thus far relied primarily on the conditions of homogeneity and subhomogeneity, and it has been conjectured that these can be relaxed. Our aim in this paper is to show that this is feasible for a general class of nonlinear monotone systems by deriving convergence results in which simple properties of the undelayed system lead to delay-independent stability. In particular, one of our results shows that if the undelayed system has a convergent trajectory that is unbounded in all components as t→-∞ then the system is globally asymptotically stable for arbitrary bounded time-varying delays. This follows from a more general result derived in the paper that allows to quantify delay-independent regions of attraction, which can be used to prove global asymptotic stability for various classes of systems. These also recover various known delay-independent stability results that are discussed within the paper.
ISSN: 0018-9286
DOI: 10.1109/TAC.2015.2498137
Rights: © 2015 IEEE.
Type: Article
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