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Zbl 0999.94577
Wu, Chai Wah
Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion, and observer design. (English)
[J] IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 48, No.10, 1257-1261 (2001). ISSN 1057-7122

Summary: It has been shown that synchronization between two nonlinear systems can be studied as a control-theory problem. We show that this relationship can be extended to synchronization in arbitrary coupled arrays of nonlinear systems. In particular, we use several well-known stability conditions to obtain synchronization criteria in arbitrarily coupled arrays: the passivity criterion, the circle criterion and a result on observer design of Lipschitz nonlinear systems. We also study how these synchronization criteria depend on the topology of the coupled networks. In particular, we show that synchronization is improved by using nonlocal connections or introducing random connections.

MSC 2000:: *94C05 Analytic circuit theory
34C60 Applications of qualitative theory of ODE
93D05 Lyapunov and other classical stabilities of control systems
93D30 Scalar and vector Lyapunov functions
94C15 Appl. of graph theory to circuits and networks
93C10 Nonlinear control systems

Keywords: algebraic connectivity; nonlinear control; random graphs; synchronization of chaos; coupled arrays of nonlinear systems; passivity criterion; circle criterion; observer

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