On Structural Rank and Resilience of Sparsity Patterns

Belabbas, Mohamed-Ali; Chen, Xudong; Zelazo, Daniel

doi:10.1109/tac.2022.3212013

Cited by 1 publication

(1 citation statement)

References 33 publications

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“…The result of Theorem 3.1 still holds if the incidence matrix is replaced with a different coupling matrix, say 𝐹 ∈ ℝ 𝜇×𝜈 , as long as there is a vector 0 ≠ 𝑣 ∈ ℝ 𝜇 such that 𝑣 𝐹 = 0. Such generalizations of a MAS were recently discussed in (Belabbas et al, 2021), but are also included in works considering, for example, distributed function calculation in MAS (Sundaram and Hadjicostis, 2008).…”

Section: Arbitrary Symmetric Couplingmentioning

confidence: 99%

On the Internal Stability of Diffusively Coupled Multi-Agent Systems and the Dangers of Cancel Culture

Barkai¹,

Mirkin²,

Zelazo³

2022

Preprint

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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.

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Section: Arbitrary Symmetric Couplingmentioning

confidence: 99%