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Stability Analysis of Monotone Systems via Max-Separable Lyapunov Functions
ABB Corp Res Ctr, S-72226 Vasteras, Sweden..
Univ Groningen, Johann Bernoulli Inst Math & Comp Sci, NL-9712 CP Groningen, Netherlands..
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 3, p. 643-656Article in journal (Refereed) Published
Abstract [en]

We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies the existence of a max-separable Lyapunov function on a compact set; second, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and insensitivity to time delays. This paper establishes that for monotone nonlinear systems, equivalence holds between asymptotic stability, the existence of a max-separable Lyapunov function, D-stability, and insensitivity to bounded and unbounded time-varying delays. In particular, a new and general notion of D-stability for monotone nonlinear systems is discussed, and a set of necessary and sufficient conditions for delay-independent stability are derived. Examples show how the results extend the state of the art.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 63, no 3, p. 643-656
Keyword [en]
Delay systems, D-stability, Lyapunov methods, monotone systems, positive systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-225290DOI: 10.1109/TAC.2017.2727282ISI: 000426276500003Scopus ID: 2-s2.0-85028940919OAI: oai:DiVA.org:kth-225290DiVA, id: diva2:1194649
Note

QC 20180403

Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-04-03Bibliographically approved

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