On Group Synchronization for Interacting Clusters of Heterogeneous Systems

This paper investigates group synchronization for multiple interacting clusters of nonidentical systems that are linearly or nonlinearly coupled. By observing the structure of the coupling topology, a Lyapunov function-based approach is proposed to deal with the case of linear systems which are linearly coupled in the framework of directed topology. Such an analysis is then further extended to tackle the case of nonlinear systems in a similar framework. Moreover, the case of nonlinear systems which are nonlinearly coupled is also addressed, however, in the framework of undirected coupling topology. For all these cases, a consistent conclusion is made that group synchronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further, the intra-cluster coupling strengths are sufficiently strong. Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.