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Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion, and observer design. (English) Zbl 0999.94577
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:
94C05Analytic circuit theory
34C60Qualitative investigation and simulation of models (ODE)
93D05Lyapunov and other classical stabilities of control systems
93D30Scalar and vector Lyapunov functions
94C15Applications of graph theory to circuits and networks
93C10Nonlinear control systems