Nonnegative edge consensus of complex networks with time delays

Differing from the existing literature about nodes' consensus, this paper focus on consensus taking place on the edges of complex network. with time delay. Firstly, the coupling protocol with time delays is given. It's worth pointing out that considering about the physically meaning, the edges must be nonnegative to make sense of the world. Then we obtain some criteria for guaranteeing the edge consensus of the proposed complex dynamical network by using linear matrix inequality, algebraic graph theory and ordinary differential equations. Finally, several examples are presented to show the effectiveness and correction of the theoretical results.