##### Generalized Nyquist Consensus Condition for Linear Multi-Agent Systems with Heterogeneous Delays

###### Estimation and Control of Networked Systems, Volume # 1 | Part# 1

**Location:**Cultural Center, Don Orione Artigianelli, Italy

**National Organizing Committee Chair:**Schenato, Luca

**International Program Committee Chair:**Johansson, Karl Henrik, Ozdaglar, Asu

**Conference Editor:**Cenedese, Angelo, Johansson, Karl Henrik, Ozdaglar, Asu, Zampieri, Sandro

Authors

Muenz, Ulrich; Papachristodoulou, Antonis; Allgower, Frank

Digital Object Identifier (DOI)

10.3182/20090924-3-IT-4005.00005

Page Numbers:

24-29

Index Terms

Consensus problems; Control with communication constraints (quantization effects etc); Multivehicle systems, flocking

Abstract

We study robust consensus of linear Multi-Agent Systems (MAS) with heterogeneous delays. We provide a very accurate set-valued condition that guarantees consensus for arbitrary bounded delays and arbitrary connected topologies. This condition is proven using the generalized Nyquist criterion. From the set-valued condition, an explicit analytical formula is derived for single integrator MAS. In this publication, the delays affect both the agent's own state and its neighbor's state; and we assume that the delay of the agent's own state and its neighbor's state are different, e.g. due to a combination of computation delays, which affect both states, and transmission delays, which only affect the neighbor's state.

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