## Abstract

We consider consensus algorithms for multi-agent networks with discrete-time linear identical MIMO agents. The agents may be of arbitrary order, the interaction topology may be time-varying and the couplings may be nonlinear and

uncertain, however assumed to satisfy a slope restriction or, more generally, quadratic constraint. Using the discrete-time version of the KYP Lemma (referred to as the Kalman-Szeg¨o Lemma), we derive a criterion which provide consensus in such a network for any uncertain couplings from the mentioned class. This criterion is close in spirit to the celebrated Tsypkin criterion for discrete time Lurie system.

uncertain, however assumed to satisfy a slope restriction or, more generally, quadratic constraint. Using the discrete-time version of the KYP Lemma (referred to as the Kalman-Szeg¨o Lemma), we derive a criterion which provide consensus in such a network for any uncertain couplings from the mentioned class. This criterion is close in spirit to the celebrated Tsypkin criterion for discrete time Lurie system.

Original language | English |
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Title of host publication | Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems |

Pages | 513-519 |

Number of pages | 7 |

Publication status | Published - 2014 |

Event | 21th International Symposium on Mathematical Theory of Networks and Systems (MTNS) - Groningen, Netherlands Duration: 7-Jul-2014 → 11-Jul-2014 |

### Conference

Conference | 21th International Symposium on Mathematical Theory of Networks and Systems (MTNS) |
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Country | Netherlands |

City | Groningen |

Period | 07/07/2014 → 11/07/2014 |