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Scaled bipartite consensus of cooperative-antagonistic multi-agent systems via joint-holonomic hybrid distributed protocol

This paper focuses on scaled bipartite consensus problem of multi-agent systems with antagonistic interactions under impulsive framework. A novel hybrid distributed protocol is adopted, where the Laplace matrix is divided into two parts based on the relationships between agents. For the cooperative-antagonistic network, this paper assumes that the communications among aligned agents are continuous-time, while divisional agents only communicate with each other in the discrete time. Besides, considering the fact that common bipartite consensus is too extreme, here we study the scaled bipartite consensus of multi-agent signed network. Furthermore, some sufficient conditions concerning delayed impulses and topology structure are derived to guarantee the scaled bipartite consensus by utilizing graph theory. At last, the efficiency of our theoretical result is demonstrated by a numerical example.