On the internal stability of diffusively coupled multi-agent systems and the dangers of cancel culture

Gal Barkai, Leonid Mirkin, Daniel Zelazo

Research output: Contribution to journalArticlepeer-review

Abstract

We study internal stability in the context of diffusively-coupled control architectures, common in multi-agent systems (i.e. the celebrated consensus protocol), for linear time-invariant agents. We derive a condition under which the system cannot be stabilized by any controller from that class. In the finite-dimensional case the condition states that diffusive controllers cannot stabilize agents that share common unstable dynamics, directions included. This class always contains the group of homogeneous unstable agents, like integrators. We argue that the underlying reason is intrinsic cancellations of unstable agent dynamics by such controllers, even static ones, where directional properties play a key role. The intrinsic lack of internal stability explains the notorious behavior of some distributed control protocols when affected by measurement noise or exogenous disturbances.

Original languageEnglish
Article number111158
JournalAutomatica
Volume155
DOIs
StatePublished - Sep 2023

Keywords

  • Controller constraints and structure
  • Multi-agent systems
  • Stability

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Control and Systems Engineering

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