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Local Lyapunov Functions for Consensus in Switching Nonlinear Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0003-0177-1993
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 12, p. 6466-6472Article in journal (Refereed) Published
Abstract [en]

This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first theorem, formulated in terms of the states of individual agents, and the second theorem, formulated in terms of the pairwise states for pairs of agents, can be interpreted as variants of Lyapunov's second method. The two theorems complement each other; the second provides stronger convergence results under weaker graph topology assumptions, whereas the first often can be applied in a wider context in terms of the structure of the right-hand sides of the systems. The second theorem also sheds some new light on well-known results for consensus of nonlinear systems where the right-hand sides of the agents' dynamics are convex combinations of directions to neighboring agents. For such systems, instead of proving consensus by using the theory of contracting convex sets, a local quadratic Lyapunov function can be used.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017. Vol. 62, no 12, p. 6466-6472
Keyword [en]
Consensus, multi-agent systems, nonlinear systems, switched systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-220473DOI: 10.1109/TAC.2017.2652302ISI: 000417090000035OAI: oai:DiVA.org:kth-220473DiVA, id: diva2:1170487
Note

QC 20180103

Available from: 2018-01-03 Created: 2018-01-03 Last updated: 2018-01-03Bibliographically approved

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Hu, Xiaoming

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