Bipartite consensus problems of directed signed networks with saturating input

This paper studies the bipartite consensus problems for directed signed networks under saturation constraints. A distributed control protocol is designed for each agent that can be described as a neutrally stable system. With the right eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, we propose a model transformation, with which the bipartite consensus problems can be equivalently transformed into the asymptotic stability problems under the structurally balanced case. The convergence of our designed protocol is proved by the Lyapunov stability theorem, which shows that the signed network subject to saturation constraints under structural balance and detailed balance communication topology can achieve bipartite consensus. In addition, we demonstrate the effectiveness of our results via a numerical example.