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Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks

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Abstract

This paper examines the global asymptotical stability of the phase synchronous dynamical networks composed by a class of nonlinear pendulum-like systems with multiple equilibria. Sufficient conditions for the determination of global asymptotical stability are given in terms of linear matrix inequalities (LMIs). Furthermore, a concept of generalized synchronization is introduced, and the criterion of which is proposed in a simple form. Those results are of particular convenience for networks that possess large numbers of nodes, and they can be used to discuss controller design problems as well. Numerical simulations and analytical results are in excellent agreement with each other.

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Authors and Affiliations

  1. State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    ShiYun Xu & Ying Yang

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  1. ShiYun Xu
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  2. Ying Yang
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Correspondence to ShiYun Xu.

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Xu, S., Yang, Y. Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks. Nonlinear Dyn 59, 485–496 (2010). https://doi.org/10.1007/s11071-009-9555-3

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  • DOI: https://doi.org/10.1007/s11071-009-9555-3

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