Algebraic criteria for consensus problems of general linear multi-agent systems with switching topology.

*(English)*Zbl 1395.93029Summary: This paper considers leaderless consensus problem and leader-following consensus problem for general linear multi-agent systems with switching interaction topology. Based on the relative states of the neighboring agents, two distributed control protocols are presented. By investigating the null space of a group of Riccati equations, algebraic criteria for the consensus problems are established, and further discussions on the preconditions of the theorems are proposed. Numerical simulations on multi-agent systems are presented to demonstrate the efficiency of our criteria.

##### MSC:

93A13 | Hierarchical systems |

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93B25 | Algebraic methods |

##### Keywords:

leaderless consensus problem; leader-following consensus problem; linear multi-agent systems; criteria; algebraic criteria
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\textit{B. Zhang} and \textit{Y. Jia}, J. Franklin Inst. 352, No. 4, 1521--1540 (2015; Zbl 1395.93029)

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