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Global asymptotical stability and generalized synchronization of phase synchronous dynamical networks. (English) Zbl 1183.70039
Summary: 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.

70K20Stability of nonlinear oscillations (general mechanics)
93D20Asymptotic stability of control systems
Full Text: DOI
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