Bipartite Consensus Using Both Direct and Indirect Information Under Signed Digraphs

Both direct and indirect information is considered for bipartite consensus of single-integrator multi-agent systems under signed digraphs. Two types of protocols based on information from indirectly connected agents are designed for each agent, respectively. By using the shortest directed paths, the concept of variant d-path Laplacian is introduced into signed digraphs, and then the closed-loop system is analyzed. Sufficient conditions for ensuring bipartite consensus are given. Further, if the original signed digraph and newly formed signed digraph are both weight balanced, agents may converge with a faster speed. Finally, examples and simulations are attached to verify theoretical results.