The optimal pinning node selection for multi-agent flocking is a NP-hard
problem. The current pinning node selection strategies mainly depend on
complex network node characteristics which are lack of rigorous
mathematical proof for flocking control. This paper studies the effect
and selection strategy of pinning node based on matrix eigenvalue
theory. Firstly, the effect on the eigenvalue of Laplacian matrix by
pinning node is analyzed. Secondly, the synchronization index which
reflects topology uniformity of multi-agent system is proposed to exert
maximum influence on the system synchronizability. A practicable optimal
pinning node selection method based on synchronization index is proposed
and analyzed by the eigenvalue perturbation method. Finally, the
simulations show the rate of system convergence by using optimal
synchronizability pinning node is better than the maximum degree
centrality.