Finite-time Asymmetric Bipartite Consensus for Signed Networks of Dynamic Agents

This paper addresses the finite-time asymmetric bipartite consensus problem for multi-agent systems (MAS) associated with signed graphs. Different from bipartite consensus in the previous literatures, asymmetric bipartite consensus means that the states of all agents will converge to two values with different signs and modulus. Two distinct nonlinear consensus control protocols are constructed for the considered system to achieve the finite-time asymmetric bipartite consensus and the fixed-time asymmetric bipartite consensus, respectively. Under the first proposed protocol, it is shown that within a finite time, the considered system can realize asymmetric bipartite consensus. To strengthen the obtained result, the second protocol is proposed, which guarantees that all agents could achieve the asymmetric bipartite consensus in fixed time, that is, the finite-time consensus can be reached before a settling time which is irrelevant with the initial states of the agents. Finally, numerical simulations are given to verify effectiveness of the proposed consensus control protocols.

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