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Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2014 (English)In: 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), 2014Conference paper, Oral presentation only (Refereed)
Abstract [en]

We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is based on an extension of a delay-independent stability result for monotone systems under constant delays by Smith to systems with bounded heterogenous time-varying delays. Under the additional assumption of positivity and sub-homogenousvector fields, we establish the aforementioned delay insensitivity property and derive a novel test for global asymptotic stability. If the system has a unique equilibrium point in the positive orthant, we prove that our stability test is necessary and sufficient. Specialized to positive linear systems, our results extend and sharpen existing results from the literature.

Place, publisher, year, edition, pages
2014.
Keyword [en]
Monotone system, Positive system, time-varying delays, Delay systems, Stability
National Category
Engineering and Technology Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-154620OAI: oai:DiVA.org:kth-154620DiVA: diva2:758281
Conference
21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), July 7-11, 2014. Groningen, The Netherlands
Note

QC 20150327

Available from: 2014-10-26 Created: 2014-10-26 Last updated: 2015-03-27Bibliographically approved

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Feyzmahdavian, Hamid RezaCharalambous, ThemistoklisJohansson, Mikael
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