Leader-following consensus of second-order agents with multiple time-varying delays.

*(English)*Zbl 1205.93056Summary: A leader-following consensus problem of second-order multi-agent systems with fixed and switching topologies as well as non-uniform time-varying delays is considered. For the case of fixed topology, a necessary and sufficient condition is obtained. For the case of switching topology, a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large. We not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate. An example with simulation is presented to illustrate the theoretical results.

##### MSC:

93B52 | Feedback control |

93D20 | Asymptotic stability in control theory |

93C35 | Multivariable systems, multidimensional control systems |

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\textit{W. Zhu} and \textit{D. Cheng}, Automatica 46, No. 12, 1994--1999 (2010; Zbl 1205.93056)

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