Paper:

# Finite-Time Consensus of Double-Integrator Multi-Agent Systems with Time-Varying Directed Topologies

## Fang Wang^{*}, Xin Chen^{**, †}, and Yong He^{**}

^{*}School of Information Science & Engineering, Central South University

Changsha, Hunan 410083, China

^{**}School of Automation, China University of Geosciences

Wuhan, Hubei 430074, China

^{†}Corresponding author

The finite-time consensus problem for double-integrator multi-agent systems (MASs) is studied using time-varying directed topologies. In detail, a distributed finite-time control protocol is designed to achieve the weighted average consensus on the basis of both relative position and relative velocity measurements by utilizing a homogeneous control technique. Then, on the basis of graph theory, homogeneity with dilation and LaSalle’s invariance principle, the designed finite-time consensus protocol ensures finite-time convergence to a consensus in the time-varying directed topologies without a global leader. Finally, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.

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