Abstract
This paper investigates a derivative-free control scheme called the single-delay Proportional-Retarded (PR) protocol to achieve fast consensus in a multi-agent system (MAS) with double-integrator agent dynamics. The PR protocol intentionally introduces a delay in the feedback loop to create a derivative-like mechanism that relies only on position measurements, thus providing high reactivity on the system while mitigating undesirable noise effects. The main result shows how the PR parameters must be tuned, subject to the MAS topology, to effectively place the spectral abscissa of the collective dynamics at a desired locus with the purpose of achieving fast consensus.
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