ASYMPTOTIC STABILITY AND DECAY RATES OF HOMOGENEOUS POSITIVE SYSTEMS WITH BOUNDED AND UNBOUNDED DELAYS
2014 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 52, no 4, 2623-2650 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2014. Vol. 52, no 4, 2623-2650 p.
monotone system, positive system, homogeneous system, time-varying delay
IdentifiersURN: urn:nbn:se:kth:diva-153295DOI: 10.1137/130943340ISI: 000341575600024ScopusID: 2-s2.0-84906810255OAI: oai:DiVA.org:kth-153295DiVA: diva2:752406
QC 201410032014-10-032014-10-032014-10-03Bibliographically approved