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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] $ (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. [ABSTRACT FROM AUTHOR]

We investigate scaled group consensus problems of high-order multi-agent systems with directed information exchanges. As one of multiple consensus, the scaled group consensus focuses on both cooperations and competitions among multi-agent sub-networks and cooperations among agents belonging to a sub-network. Two distributed protocols are designed to solve the scaled group consensus problems. The (generalised) Routh–Hurwitz stability criterion and matrix theory are utilised to establish necessary and sufficient conditions guaranteeing the agents reaching the scaled group consensus. Finally, several simulations are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

We discuss a new consensus problem – a group consensus problem – in networks of dynamic agents. For a complex network consisting of several sub-networks owing to physical quantities or task distributions, it is concerned with this case that the agents in a sub-network share a consistent value while there is no agreement between any two sub-networks. When the information exchange is directed, a novel consensus protocol is designed to solve the group consensus problem. The convergence analysis is discussed and several criteria are established based on graph theories and matrix theories. Simulation results are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]