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Article: Stability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method
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TitleStability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method
 
AuthorsZhao, J2
Hill, DJ1
Liu, T3
 
KeywordsDynamical Networks
Graph
Synchronization
V-Stability
 
Issue Date2011
 
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
 
CitationAutomatica, 2011, v. 47 n. 12, p. 2615-2625 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.automatica.2011.09.012
 
AbstractGlobal asymptotic stability of general dynamical networks with non-identical nodes is studied by introducing multiple V-Lyapunov functions. In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear. A stability criterion is proposed in terms of matrix norms and eigenvalues of some lower-dimensional matrices. Based on this criterion, an optimization problem is formed whose solution can be used to test global asymptotic stability. We also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple V-Lyapunov functions. The control action is regarded as a re-shape of outer coupling topology and the associated controllers are designed. In particular, a method of adding or removing a certain number of links is proposed. Stability analysis of coupled non-identical Lorenz systems and a design example are also given to illustrate the proposed method. © 2011 Elsevier Ltd. All rights reserved.
 
ISSN0005-1098
2013 Impact Factor: 3.132
2013 SCImago Journal Rankings: 2.717
 
DOIhttp://dx.doi.org/10.1016/j.automatica.2011.09.012
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorZhao, J
 
dc.contributor.authorHill, DJ
 
dc.contributor.authorLiu, T
 
dc.date.accessioned2012-10-25T04:54:30Z
 
dc.date.available2012-10-25T04:54:30Z
 
dc.date.issued2011
 
dc.description.abstractGlobal asymptotic stability of general dynamical networks with non-identical nodes is studied by introducing multiple V-Lyapunov functions. In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear. A stability criterion is proposed in terms of matrix norms and eigenvalues of some lower-dimensional matrices. Based on this criterion, an optimization problem is formed whose solution can be used to test global asymptotic stability. We also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple V-Lyapunov functions. The control action is regarded as a re-shape of outer coupling topology and the associated controllers are designed. In particular, a method of adding or removing a certain number of links is proposed. Stability analysis of coupled non-identical Lorenz systems and a design example are also given to illustrate the proposed method. © 2011 Elsevier Ltd. All rights reserved.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationAutomatica, 2011, v. 47 n. 12, p. 2615-2625 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.automatica.2011.09.012
 
dc.identifier.citeulike9909168
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.automatica.2011.09.012
 
dc.identifier.epage2625
 
dc.identifier.issn0005-1098
2013 Impact Factor: 3.132
2013 SCImago Journal Rankings: 2.717
 
dc.identifier.issue12
 
dc.identifier.scopuseid_2-s2.0-81155148181
 
dc.identifier.spage2615
 
dc.identifier.urihttp://hdl.handle.net/10722/169733
 
dc.identifier.volume47
 
dc.languageeng
 
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
 
dc.publisher.placeUnited Kingdom
 
dc.relation.ispartofAutomatica
 
dc.relation.referencesReferences in Scopus
 
dc.subjectDynamical Networks
 
dc.subjectGraph
 
dc.subjectSynchronization
 
dc.subjectV-Stability
 
dc.titleStability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method
 
dc.typeArticle
 
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Author Affiliations
  1. University of Sydney
  2. Northeastern University China
  3. Australian National University