Bipartite output synchronization of linear heterogeneous multi-agent systems via output feedback

In this paper we investigate bipartite output synchronization of a group of linear heterogeneous agents communicating their outputs over a signed graph. Our multi-agent system contains N followers and one leader and we aim to achieve bipartite output synchronization to the output of the leader. By the bipartite output synchronization, we mean output synchronization in the modulus; while the modulus is the same for all the agents, the signs could be different. Assuming that the communication graph is structurally balanced, we show that the bipartite output synchronization over the signed graph is equivalent to the classical output synchronization over an unsigned graph whose adjacency matrix is the element-wise absolute value of the adjacency matrix of the signed graph. We propose explicit output-feedback controller in this paper and illustrate our theoretical development by a simulation example.