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Pinning synchronization of time-varying polytopic directed stochastic networks. (English) Zbl 1235.34160

Summary: In this Letter, pinning synchronization of a directed network with Markovian jump (DNMJ) and nonlinear perturbations is considered. By analyzing the structure of the network, a detailed pinning scheme is given to ensure the synchronization of all nodes in a DNMJ. This pinning scheme can overcome those difficulties on deciding which nodes needs to be pinned. This scheme can also identify the exact least number of pinned nodes for a DNMJ model. In addition, the time-varying polytopic directed network with Markovian jump is discussed. Finally, examples are provided to illustrate the effectiveness of the gained criteria.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
90B15 Stochastic network models in operations research
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