Abstract
This paper extends the graph filtering method to the group consensus of multi-agent systems. For in-degree balanced graphs, sufficient and necessary conditions of the finite time group consensus and the asymptotic group consensus are given, respectively. And the exact convergence rate of the asymptotic group consensus is discussed. Furthermore, for the case of estimated graphs, two explicit design methods of the periodic control protocol are proposed, and the optimal control sequence is given to achieve the fastest convergence in the worst case. Finally, numerical simulations are presented to verify the efficiency of theoretical results.
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