GriD-LMIA: A Gridding-Based Assembler for Solving Differentiable Parameter-Dependent Linear Matrix Inequalities

[2608.03175] GriD-LMIA: A Gridding-Based Assembler for Solving Differentiable Parameter-Dependent Linear Matrix Inequalities Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2608.03175 (eess) [Submitted on 4 Aug 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: GriD-LMIA: A Gridding-Based Assembler for Solving Differentiable Parameter-Dependent Linear Matrix Inequalities Authors: Yicheng Xu , Faryar Jabbari View PDF HTML (experimental) Abstract: Parameter-dependent linear matrix inequalities (PD-LMIs) require holding over a continuous domain. When the scheduling parameters vary with time, derivatives of parameter-dependent decisions may also enter the conditions. Since semidefinite programming solvers require finitely many constraints, we introduce GriD-LMIA, the Gridding-based Differentiable PD-LMI Assembler. It converts the conditions that need to hold on a continuous domain into finitely many sufficient LMIs in MATLAB. It first partitions the domain with a hyper-rectangular grid and represents known data and decisions on each cell with tensor Bernstein polynomials. The package exports direct Bernstein, Pólya-elevated, and sum-of-squares-based certificates through YALMIP. Examples are given to examine the balance among grid density, decision degree, and certificate choice. Subjects: Systems and Control (eess.SY) ; Mathematical Software (cs.MS) Cite as: arXiv:2608.03175 [eess.SY] (or arXiv:2608.03175v2 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2608.03175 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yicheng Xu [ view email ] [v1] Tue, 4 Aug 2026 06:07:28 UTC (223 KB) [v2] Tue, 25 Aug 2026 04:03:48 UTC (1,039 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-08 Change to browse by: cs cs.MS 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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