Asymptotic stability and decay rates of homogeneous positive systems with bounded and unbounded delays

Hamid Reza Feyzmahdavian, Themistoklis Charalambous, Mikael Johansson

Research output: Contribution to journalArticleScientificpeer-review

36 Citations (Scopus)

Abstract

There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, we present a necessary and sufficient condition for delay-independent stability of continuous-time positive systems whose vector fields are cooperative and homogeneous. We show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays. For various classes of time delays, we are able to derive explicit expressions that quantify the decay rates of positive systems. We also provide the corresponding counterparts for discrete-time positive systems whose vector fields are nondecreasing and homogeneous.

Original languageEnglish
Pages (from-to)2623-2650
Number of pages28
JournalSIAM Journal on Control and Optimization
Volume52
Issue number4
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Homogeneous system
  • Monotone system
  • Positive system
  • Time-varying delay

Fingerprint Dive into the research topics of 'Asymptotic stability and decay rates of homogeneous positive systems with bounded and unbounded delays'. Together they form a unique fingerprint.

Cite this