On the state agreement problem for multiple nonlinear dynamical systems

Authors:	Lin Zhiyun, University of Toronto, Canada Francis Bruce, University of Toronto, Canada Maggiore Manfredi, University of Toronto, Canada
Topic:	5.4 Large Scale Complex Systems
Session:	Large Scale Complex Systems I- Theory
Keywords:	Coupled nonlinear systems, interconnection, asymptotic stability

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 sub-tangentiality 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.