Abstract
The master stability equations for a complex dynamical network with general topology are obtained. Compared to prior work, we remove almost all the restrictions on the graph of the network. The coupling configuration matrix is not necessarily diagonalizable, the coupling coefficients are not necessarily nonnegative, and the graph of the network can be directed. These new master stability equations as for those in the previous studies are still very effective in analyzing the stability of complex dynamical networks in terms of synchronization to a manifold. We present some new observations on stability. A new concept heavily connected, which can be regarded as the generalization of both connected for an undirected graph and strong connected for a directed graph, is proposed. The proofs of the two main theorems are very short but can substitute many of those in the literature.
| Original language | English |
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| Title of host publication | Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC |
| Publisher | Elsevier - International Federation of Automatic Control (IFAC) |
| Edition | 1 PART 1 |
| ISBN (Print) | 9783902661005 |
| DOIs | |
| Publication status | Published - 2008 |
| Externally published | Yes |
| Event | International Federation of Automatic Control World Congress 2008 - Convention and Exhibition Center, Seoul, Korea, South Duration: 6 Jul 2008 → 11 Jul 2008 Conference number: 17th https://web.archive.org/web/20080609024600/http://www.ifac2008.org/ |
Publication series
| Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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| Number | 1 PART 1 |
| Volume | 17 |
| ISSN (Print) | 1474-6670 |
Conference
| Conference | International Federation of Automatic Control World Congress 2008 |
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| Abbreviated title | IFAC 2008 |
| Country/Territory | Korea, South |
| City | Seoul |
| Period | 6/07/08 → 11/07/08 |
| Internet address |
Keywords
- Control of networks
- Cooperative systems
- Nonlinear systems