Robust Stabilization of LPV Sampled-Data Systems via Quadratic Polynomial Conditions

Robust Stabilization of LPV Sampled-Data Systems via Quadratic Polynomial Conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Robust Stabilization of LPV Sampled-Data Systems via Quadratic Polynomial Conditions Lucas A. L. Oliveira, Marcus V. C. Barbosa, Koffi M. D. Motchon, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7642613/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Jan, 2026 Read the published version in Journal of Control, Automation and Electrical Systems → Version 1 posted 11 You are reading this latest preprint version Abstract This work addresses the robust stabilization of linear parameter-varying (LPV) systems with state feedback, using linear matrix inequalities (LMIs) for the synthesis of sampled-data controllers. Using the input-delay approach, we propose a looped-functional whose time derivative is a quadratic polynomial. The negativity of this polynomial must be ensured to certify the closed-loop stability. Pólya's Theorem is then employed to ensure the negativity of quadratic functions, yielding new and less conservative convex conditions for controller synthesis under time-varying sampling intervals. Numerical examples illustrate the effectiveness of the proposed technique, showing that the new design conditions outperform those reported in recent literature. Finally, the proposed design conditions are adapted to handle quasi-LPV systems and applied to a nonlinear level control system. Experimental tests on the system illustrate the performance of the designed controller for different time-varying sampling intervals. Sampled-data control LPV systems Negative definiteness of quadratic functions Robust stabilization Lyapunov-Krasovskii looped-functionals Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Jan, 2026 Read the published version in Journal of Control, Automation and Electrical Systems → Version 1 posted Editorial decision: Revision requested 17 Nov, 2025 Reviews received at journal 10 Nov, 2025 Reviews received at journal 31 Oct, 2025 Reviewers agreed at journal 27 Oct, 2025 Reviewers agreed at journal 13 Oct, 2025 Reviews received at journal 27 Sep, 2025 Reviewers agreed at journal 24 Sep, 2025 Reviewers invited by journal 23 Sep, 2025 Editor assigned by journal 20 Sep, 2025 Submission checks completed at journal 19 Sep, 2025 First submitted to journal 17 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7642613","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":524445770,"identity":"da1af3b8-b5da-4a28-b806-85f509916c4b","order_by":0,"name":"Lucas A. L. 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