Bipartite consensus tracking of second-order fractional-order multi-agent systems on directed signed graphs

This paper studies the bipartite consensus tracking problems of fractional-order multi-agent systems on directed signed graphs. Each agent is modelled as a second-order fractional-order dynamics with the order belonging to (0,1], and the cooperative and competitive interactions between the agents coexist in the systems. Two distributed bipartite consensus tracking protocols are proposed for the systems based on continuous information and sampled information, respectively. Under the assumption that the directed signed graph is structurally balanced, it is shown that the second-order fractional-order multi-agent systems can achieve the bipartite consensus tracking if the feedback coefficients are chosen appropriately. Finally, several simulations are provided to verify the effectiveness of the theoretical results.