Distributed Finite-time Differentiator for Multi-agent Systems Under Directed Graph

Abstract

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.