Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and time delay

Abstract

This paper investigates the synchronization problem for coupled nonlinear systems in which antagonistic interactions and bounded time delay coexist. In order to make the network achieve bipartite synchronization, we design a pinning scheme to pin a part of agents such that the network is connected. Under the assumptions that the signed graph is structurally balanced, the nonlinear system satisfies one-sided Lipschitz and quadratic inner-boundedness conditions, we derive some bipartite synchronization conditions for non-differentiable and differentiable coupling delays respectively. All criteria are presented as linear matrix inequalities. Finally, we present two numerical examples about neural network to illustrate the effectiveness of the obtained results.