In this paper, the projective group consensus issue for second order multi-agent systems (MASs) in directed graphs with a dynamic leader is investigated. The proposed projective group consensus with arbitrary parameter includes traditional consensus, reverse group consensus and cluster consensus as its special cases. Novel distributed control protocols are designed to obtain projective group consensus without analyzing signed directed graph as in most current literatures on bipartite consensus problem. On the basis of Lyapunov stability property, algebraic graph and some necessary matrix theory, sufficient conditions for delay and delay-free cases are derived. Finally, simulations of nonlinear chaotic MASs are adopted to testify the theoretical results.

在本文中，研究了带有动态前导的有向图中二阶多智能体系统（MAS）的射影群共识问题。拟议的带有任意参数的射影群体共识包括传统共识，反向群体共识和聚类共识作为特例。新颖的分布式控制协议旨在获得射影组共识，而无需像大多数有关二分共识问题的最新文献那样分析有向图。基于Lyapunov稳定性，代数图和一些必要的矩阵理论，得出了时滞和无时滞情况的充分条件。最后，通过对非线性混沌MAS的仿真来验证理论结果。