On pining synchronization of switching dynamical networks

Ponente(s): Isaac Leonel López García, Dr. Juan Gonzalo Barajas Ramírez

We investigate pinning synchronization in networks with changing structure. The changes we considered are only in the set of links, according to an arbitrary switching law that determines which topology is active at each instant in time among a finite set of admissible topologies. The control objective is to synchronize the network under arbitrary switching, i.e., to stabilize the solution of the network where the states of all nodes evolve at unison, independently of the switching on topologies. We show how the changes in the topology can be considered to select which nodes to control and design appropriate gains for a local feedback control loop to ensure network synchronization. We use a common Lyapunov function to demonstrate the stability of the synchronization solution. We illustrate our results with numerical simulations of a switching network of Lorenz systems.