Analysis of Structural Balance and Distributed Control for High-Order Signed Networks

This article investigates the problems of structural balance and distributed control for a high-order signed network with generic linear dynamics. A novel approach is proposed to analyze the structural balance of a general network based on the strongly connected components of the topology graph and the Frobenius normal form of the adjacency matrix. To address the distributed control of high-order signed networks, both state-feedback and observer-type algorithms are developed on the basis of low-gain strategies, where a unified framework is presented to construct full- or reduced-order observers. The dynamical behaviors of the signed network under the proposed algorithms are systematically explored, where the nontrivial final network state is computed by employing an eigenvector-based approach. The theoretical results are illustrated by numerical examples.