New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides. (English) Zbl 1258.93007
Summary: In this paper, we study synchronization of networks of linearly coupled dynamical systems. The node dynamics of the network can be very general, which may not satisfy the QUAD condition. We derive sufficient conditions for synchronization, which can be regarded as extensions of previous results. These results can be employed to networks of coupled systems, of which, in particular, the node dynamics have non-Lipschitz or even discontinuous right-hand sides. We also give several corollaries where the synchronization of some specific non-QUAD systems can be deduced. As an application, we propose a scheme to realize synchronization of coupled switching systems via coupling the signals which drive the switchings. Examples with numerical simulations are also provided to illustrate the theoretical results.
MSC:
| 93A14 | Decentralized systems |
| 94C15 | Applications of graph theory to circuits and networks |
| 93A15 | Large-scale systems |
| 34H05 | Control problems involving ordinary differential equations |
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
Keywords:
linearly coupled systems; synchronization; non-Lipschitz right-hand sides; discontinuous right-hand sideReferences:
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