Coupled Dynamic Systems: From Structure Towards State Agreement

The state agreement problem is studied for nonlinear continuous-time systems. A general interconnection of nonlinear subsystems is treated, where the vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. With the assumption that the vector fields satisfy a certain sub-tangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. Applications of the main result are then made to the synchronization of coupled Kuramoto oscillators with time-varying interaction and to the analysis of a biochemical reaction network.