ON THE STATE AGREEMENT PROBLEM FOR MULTIPLE NONLINEAR DYNAMICAL SYSTEMS

Abstract This paper studies the state agreement problem with the objective to ensure the asymptotic coincidence of all states of multiple nonlinear dynamical systems. The coupling structure of such systems is characterized in qualitative terms by means of a suitably defined directed graph. Under a suitable subtangentiality assumption on the vector fields of the systems, we obtain a necessary and sufficient graphical condition for their state agreement via nonsmooth analysis, with the invariance principle playing a central role. As applications, we study synchronization of coupled Kuramoto oscillators and synthesis of a rendezvous controller for a multi-agent system.

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