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Local lyapunov functions for consensus in switching nonlinear systems

Thunberg, Johan LU ; Hu, Xiaoming and Gonçalves, Jorge (2017) In IEEE Transactions on Automatic Control 62(12). p.6466-6472
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 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... (More)
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. (Less)
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Contribution to journal
publication status
published
subject
in
IEEE Transactions on Automatic Control
volume
62
issue
12
pages
7 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
ISSN
0018-9286
DOI
10.1109/TAC.2017.2652302
language
Unknown
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no
id
9a03db02-0615-424e-9c5c-b37f5f2fdd58
date added to LUP
2024-09-05 14:25:42
date last changed
2024-09-20 11:49:07
@article{9a03db02-0615-424e-9c5c-b37f5f2fdd58,
  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 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.}},
  author       = {{Thunberg, Johan and Hu, Xiaoming and Gonçalves, Jorge}},
  issn         = {{0018-9286}},
  language     = {{und}},
  number       = {{12}},
  pages        = {{6466--6472}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{Local lyapunov functions for consensus in switching nonlinear systems}},
  url          = {{http://dx.doi.org/10.1109/TAC.2017.2652302}},
  doi          = {{10.1109/TAC.2017.2652302}},
  volume       = {{62}},
  year         = {{2017}},
}