3.Protocol selection for second-order consensus against disturbance

Jiamin Wang, Liqi Zhou, Dong Zhang, Jian Liu, Feng Xiao, and Yuanshi Zheng

Noticing that both the absolute and the relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the \(\mathcal{L}_2\) gains from disturbance to consensus errors. More specifically, by the orthogonal transformation technique, the analytic expression of the \(\mathcal{L}_2\) gain of a second-order multi-agent system with the absolute velocity protocol is firstly derived, followed by the counterpart with the relative velocity protocol. It is shown that both the \(\mathcal{L}_2\) gains for the absolute and the relative velocity protocols are determined only by the minimum non-zero eigenvalues of Laplacian matrices and the tunable gains of position-like and velocity-like states. Then, we establish the graph conditions to tell which protocol has better anti-disturbance capability. Moreover, we propose a two-step scheme to improve the anti-disturbance capability of second-order multi-agent systems. Finally, numerical tests are given for different types of interaction graphs.

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