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Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. (English) Zbl 1226.93014
Summary: We discuss the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader-follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. A rigorous proof is given by using the Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.

##### MSC:
 93A14 Decentralized systems 94C15 Applications of graph theory to circuits and networks 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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