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Zbl 1153.93329
Porfiri, Maurizio; di Bernardo, Mario
Criteria for global pinning-controllability of complex networks. (English)
[J] Automatica 44, No. 12, 3100-3106 (2008). ISSN 0005-1098

Summary: We study pinning-controllability of networks of coupled dynamical systems. In particular, we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network. The reference trajectory is generated by an exogenous independent oscillator, and pinned nodes are coupled to it through a linear state feedback. We describe the time evolution of the complex dynamical system in terms of the error dynamics. Thereby, we reformulate the pinning-controllability problem as a global asymptotic stability problem. By using Lyapunov-stability theory and algebraic graph theory, we establish tractable sufficient conditions for global pinning-controllability in terms of the network topology, the oscillator dynamics, and the linear state feedback.

MSC 2000:: *93B05 Controllability
93D20 Asymptotic stability of control systems
93C10 Nonlinear control systems
93D05 Lyapunov and other classical stabilities of control systems
93B11 System structure simplification

Keywords: synchronization; pinning-controllability; graphs; global stability

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Zentralblatt MATH Berlin [Germany]