Average contraction and synchronization of complex switched networks

This paper introduces an average contraction analysis for nonlinear switched systems and applies it to investigating the synchronization of complex networks of coupled systems with switching topology. For a general nonlinear system with a time-dependent switching law, a basic convergence result is presented according to average contraction analysis, and a special case where trajectories of a distributed switched system converge to a linear subspace is then investigated. Synchronization is viewed as the special case with all trajectories approaching the synchronization manifold, and is thus studied for complex networks of coupled oscillators with switching topology. It is shown that the synchronization of a complex switched network can be evaluated by the dynamics of an isolated node, the coupling strength and the time average of the smallest eigenvalue associated with the Laplacians of switching topology and the coupling fashion. Finally, numerical simulations illustrate the effectiveness of the proposed methods.