Bipartite synchronization of nonlinear network under signed digraph and switching topologies
Chang Liu, Hui Ding, Lei Zhou · 2020
The bipartite synchronization problem of nonlinear signed networks with switching topologies is considered in this paper. The node dynamics is a general Lipschitz nonlinear system and the switching signal satisfies the average dwell time condition. It is assumed that the switching directed topology is structurally balanced and always contains a directed spanning tree. By using the coordinate transform method, the bipartite synchronization error system is formulated as a switched system. Then based on algebraic graph theory and multiple Lyapunov function method, sufficient bipartite synchronization conditions are established in terms of linear matrix inequality. The obtained result indicates that the bipartite synchronization of the signed nonlinear network can always be achieved under sufficiently slow switching of network topology if the coupling strength is sufficiently large. The numerical simulations show the effectiveness of the obtained bipartite synchronization control method.