  This paper proposes a new distributed finite-time differentiator (DFD) for
multi-agent systems (MAS) under directed graph, which extends the
differentiator algorithm from the centralized case to the distributed case by
only using relative/absolute position information. By skillfully constructing a
Lyapunov function, the finite-time stability of the closed-loop system under
DFD is proved. Inspired by the duality principle of control theory, a
distributed continuous finite-time output consensus algorithm extended from DFD
for a class of leader-follower MAS is provided, which not only completely
suppresses disturbance, but also avoids chattering. Finally, several simulation
examples are given to verify the effectiveness of the DFD.
