A sharp bound on the s-energy and its applications to averaging systems

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Abstract

The s-energy is a generating function of wide applicability in network-based dynamics. We derive an (essentially) optimal bound of (3/ρs)n-1 on the s-energy of an n-agent symmetric averaging system, for any positive real s ≤ 1, where ρ is a lower bound on the nonzero weights. This is done by introducing the new dynamics of twist systems. We show how to use the new bound on the s-energy to tighten the convergence rates of systems in opinion dynamics, flocking, and synchronization.

Original languageEnglish (US)
Article number8642407
Pages (from-to)4385-4390
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume64
Issue number10
DOIs
StatePublished - Oct 2019

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Keywords

  • S-energy

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