  Noticing that both the absolute and 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 L2 gain from the
disturbance to the consensus error. More specifically, by the orthogonal
transformation technique, the analytic expression of the L2 gain of the
second-order multi-agent system with absolute velocity protocol is firstly
derived, followed by the counterpart with relative velocity protocol. It is
shown that both the L2 gains for absolute and relative velocity protocols are
determined only by the minimum non-zero eigenvalue of Laplacian matrix and the
tunable gains of the state and velocity. 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, simulations are given
to illustrate the effectiveness of our findings.
