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Local Lyapunov Functions for Consensus in Switching Nonlinear Systems

Accepted version
Peer-reviewed

Type

Article

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Authors

Thunberg, J 
Mendes Silva Goncalves, Jorge  ORCID logo  https://orcid.org/0000-0002-5228-6165
Hu, X 

Abstract

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 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.

Description

Keywords

consensus, multi-agent systems, nonlinear systems, switched systems

Journal Title

IEEE Transactions on Automatic Control

Conference Name

Journal ISSN

0018-9286
1558-2523

Volume Title

Publisher

IEEE
Sponsorship
The authors gratefully acknowledge the financial support form the Fonds National de la Recherche, Luxembourg (FNR8864515).