Generalized Nyquist Consensus Condition for Linear Multi-Agent Systems with Heterogeneous Delays
Estimation and Control of Networked Systems, Volume # 1 | Part# 1
Muenz, Ulrich; Papachristodoulou, Antonis; Allgower, Frank
Digital Object Identifier (DOI)
Consensus problems; Control with communication constraints (quantization effects etc); Multivehicle systems, flocking
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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