Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control.

*(English)*Zbl 1193.93059Summary: The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

##### MSC:

93A14 | Decentralized systems |

93C05 | Linear systems in control theory |

93D30 | Lyapunov and storage functions |

##### Keywords:

multi-agent systems; formation control; quantized control; algebraic graph theory; networked control
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\textit{D. V. Dimarogonas} and \textit{K. H. Johansson}, Automatica 46, No. 4, 695--700 (2010; Zbl 1193.93059)

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