2022
DOI: 10.48550/arxiv.2203.04215
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Multi-agent consensus over time-invariant and time-varying signed digraphs via eventual positivity

Abstract: Laplacian dynamics on signed digraphs have a richer behavior than those on nonnegative digraphs. In particular, for the so-called "repelling" signed Laplacians, the marginal stability property (needed to achieve consensus) is not guaranteed a priori and, even when it holds, it does not automatically lead to consensus, as these signed Laplacians may loose rank even in strongly connected digraphs. Furthermore, in the time-varying case, instability can occur even when switching in a family of systems each of whic… Show more

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Cited by 1 publication
(4 citation statements)
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“…The aim of this section is to summarize important properties of Laplacian matrices which will be useful in the following. Most of these results are from our previous works [3,18,19], hence they are reported here without proofs. First, Section 3.1 treats the unsigned Laplacians case; then, Section 3.2 considers the signed Laplacians case.…”
Section: Signed Graphs Letmentioning
confidence: 86%
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“…The aim of this section is to summarize important properties of Laplacian matrices which will be useful in the following. Most of these results are from our previous works [3,18,19], hence they are reported here without proofs. First, Section 3.1 treats the unsigned Laplacians case; then, Section 3.2 considers the signed Laplacians case.…”
Section: Signed Graphs Letmentioning
confidence: 86%
“…1, and Cor. 2 in [19]). Let G(A) be a signed directed graph with signed Laplacian L. Consider the following conditions:…”
Section: Signed Directed Graphs Casementioning
confidence: 99%
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