Article: Stability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method
| Title | Stability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method |
|---|---|
| Authors | Zhao, J2 Hill, DJ1 Liu, T3 |
| Keywords | Dynamical Networks Graph Synchronization V-Stability |
| Issue Date | 2011 |
| Publisher | Pergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica |
| Citation | Automatica, 2011, v. 47 n. 12, p. 2615-2625 [How to Cite?] DOI: http://dx.doi.org/10.1016/j.automatica.2011.09.012 |
| Abstract | Global 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. |
| ISSN | 0005-1098 2011 Impact Factor: 2.829 2011 SCImago Journal Rankings: 0.111 |
| DOI | http://dx.doi.org/10.1016/j.automatica.2011.09.012 |
| References | References in Scopus |
| dc.contributor.author | Zhao, J |
|---|---|
| dc.contributor.author | Hill, DJ |
| dc.contributor.author | Liu, T |
| dc.date.accessioned | 2012-10-25T04:54:30Z |
| dc.date.available | 2012-10-25T04:54:30Z |
| dc.date.issued | 2011 |
| dc.description.abstract | Global 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.nature | Link_to_subscribed_fulltext |
| dc.identifier.citation | Automatica, 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.citeulike | 9909168 |
| dc.identifier.doi | http://dx.doi.org/10.1016/j.automatica.2011.09.012 |
| dc.identifier.epage | 2625 |
| dc.identifier.issn | 0005-1098 2011 Impact Factor: 2.829 2011 SCImago Journal Rankings: 0.111 |
| dc.identifier.issue | 12 |
| dc.identifier.scopus | eid_2-s2.0-81155148181 |
| dc.identifier.spage | 2615 |
| dc.identifier.uri | http://hdl.handle.net/10722/169733 |
| dc.identifier.volume | 47 |
| dc.language | eng |
| dc.publisher | Pergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica |
| dc.publisher.place | United Kingdom |
| dc.relation.ispartof | Automatica |
| dc.relation.references | References in Scopus |
| dc.subject | Dynamical Networks |
| dc.subject | Graph |
| dc.subject | Synchronization |
| dc.subject | V-Stability |
| dc.title | Stability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method |
| dc.type | Article |
Author Affiliations
- University of Sydney
- Northeastern University China
- Australian National University