Sparse Representations of Dynamical Networks: A Coprime Factorization Approach

[2206.09945] Sparse Representations of Dynamical Networks: A Coprime Factorization Approach Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2206.09945 (eess) [Submitted on 20 Jun 2022 ( v1 ), last revised 25 Aug 2026 (this version, v8)] Title: Sparse Representations of Dynamical Networks: A Coprime Factorization Approach Authors: Şerban Sabău , Andrei Sperilă , Cristian Oară , Ali Jadbabaie View PDF HTML (experimental) Abstract: We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the structure of their component subsystems' interconnection. In doing so, we provide tractable means of shifting between different types of sparsity-preserving representations and we show how to employ these factorizations to obtain distributed implementations for stabilizing and possibly stable controllers. By formulating all these results for both discrete- and continuous-time systems, we develop specialized distributed implementations that, up to this point, were only available for networks modeled as discrete-time systems. Comments: 35 pages, 5 figures Subjects: Systems and Control (eess.SY) MSC classes: 93A14, 93B99, 93C05 Cite as: arXiv:2206.09945 [eess.SY] (or arXiv:2206.09945v8 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2206.09945 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Andrei Sperilă [ view email ] [v1] Mon, 20 Jun 2022 18:05:07 UTC (610 KB) [v2] Fri, 26 Jan 2024 08:35:02 UTC (150 KB) [v3] Tue, 13 Feb 2024 09:15:02 UTC (81 KB) [v4] Sun, 17 Nov 2024 14:08:16 UTC (81 KB) [v5] Mon, 1 Sep 2025 18:29:26 UTC (80 KB) [v6] Tue, 11 Nov 2025 15:41:05 UTC (77 KB) [v7] Sun, 30 Nov 2025 16:41:01 UTC (77 KB) [v8] Tue, 25 Aug 2026 10:05:15 UTC (72 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2022-06 Change to browse by: cs cs.SY eess References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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