Bounded synchronization of a heterogeneous complex switched network. (English) Zbl 1323.93011
Summary: This paper investigates synchronization issues of a heterogeneous complex network with a general switching topology in the sense of boundedness, when no complete synchronization manifold exists. Several sufficient conditions are established with the Lyapunov method and the differential analysis of convergence to determine the existence and estimate the convergence domain for the local and global bounded synchronization of a heterogeneous complex network. By using the consensus convergence of a switched linear system associated with the switching topology, explicit bounds of the maximum deviation between nodes are obtained in the form of a scalar inequality involving the property of the consensus convergence and the homogeneous and heterogeneous dynamics of individual nodes for the local and global cases. These analytical results are simple yet generic, which can be used to explore synchronization issues of various complex networks. Finally, a numerical simulation illustrates their effectiveness.
MSC:
| 93A14 | Decentralized systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34D06 | Synchronization of solutions to ordinary differential equations |
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