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Spectral Conditions for Stability and Stabilization of Positive Equilibria for a Class of Nonlinear Cooperative Systems
Univ Padua, Italy; Tech Univ Munich, Germany.
Univ Padua, Italy; Dartmouth Coll, NH 03755 USA.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-4142-6502
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 2, p. 402-417Article in journal (Refereed) Published
Abstract [en]

Nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication, biological, economical, and neural network applications. For this class of positive systems, we provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system. If control inputs are available, then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 63, no 2, p. 402-417
Keywords [en]
Concave systems; nonlinear cooperative systems; positive equilibrium points; stability and stabilization; subhomogeneous systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-145240DOI: 10.1109/TAC.2017.2713241ISI: 000423553000007OAI: oai:DiVA.org:liu-145240DiVA, id: diva2:1188345
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-03-07 Created: 2018-03-07 Last updated: 2018-03-23

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