Asymptotic stability of dynamical networks

In this paper, asymptotic stability of dynamical networks with non-identical nodes is investigated. Networks with fixed and switching topologies are discussed, respectively. Different Lyapunov functions for each individual node are used, and sufficient conditions for both cases are derived to guarantee asymptotic stability of such networks. The stabilizing switching signals are identified by using the convex combination method for networks with switching topology. The results obtained are not only restricted to undirected networks, but also applicable to directed networks. A numerical example of switched network is given to show the effectiveness of the proposed results.