Global Synchronization of Dynamical Networks with Non-identical Nodes: a Multiple V-Lyapunov Function Method

Abstract

The global synchronization problem for general dynamical networks with non-identical nodes is studied by introducing multiple V-Lyapunov functions. In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear. A global synchronization criterion is proposed in terms of matrix norms and eigenvalues of some lower-dimensional matrices. We also study the problem of how to achieve global synchronization by design of controllers under the scheme of multiple V-Lyapunov functions. The control action is regarded as a re-shape of outer coupling topology and the associated controllers are designed. In particular, a method of global synchronization by adding or removing a certain number of links is proposed.