Electrical Engineering and Systems Science > Systems and Control
[Submitted on 12 Oct 2022 (v1), last revised 9 May 2023 (this version, v2)]
Title:On the Internal Stability of Diffusively Coupled Multi-Agent Systems and the Dangers of Cancel Culture
View PDFAbstract: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 can not 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.
Submission history
From: Gal Barkai [view email][v1] Wed, 12 Oct 2022 12:53:27 UTC (2,650 KB)
[v2] Tue, 9 May 2023 19:21:36 UTC (831 KB)
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