A BLMI-Based Framework for Robust Stabilization of Stochastic Hybrid Systems Under Dual-Mode Uncertainties

A BLMI-Based Framework for Robust Stabilization of Stochastic Hybrid Systems Under Dual-Mode Uncertainties | 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 Article A BLMI-Based Framework for Robust Stabilization of Stochastic Hybrid Systems Under Dual-Mode Uncertainties Tao Wang, Fubo Zhu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6257186/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigates the robust stabilization problem for linear stochastic hybrid systems (SHSs) characterized by dual uncertainties: parametric variations in system matrices and bounded uncertainties in Markovian transition rates. Novel sufficient conditions for exponential mean-square stability are derived via bilinear matrix inequalities (BLMIs). A systematic methodology is proposed to design robust state-feedback controllers, eliminating reliance on exact transition rate knowledge. Numerical simulations confirm the frameworks efficacy, demonstrating its applicability in scenarios with coexisting parametric and structural uncertainties. Physical sciences/Mathematics and computing Physical sciences/Mathematics and computing/Applied mathematics Bilinear matrix inequalities (BLMIs) Robust stabilization Stochastic hybrid sys- tems (SHSs) Uncertain transition rates Markovian switching Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-6257186","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":437771394,"identity":"089ffa63-d2cd-4d39-9ba8-993822d1b2bb","order_by":0,"name":"Tao Wang","email":"","orcid":"","institution":"Huaiyin Normal University","correspondingAuthor":false,"prefix":"","firstName":"Tao","middleName":"","lastName":"Wang","suffix":""},{"id":437771395,"identity":"b945266e-7bae-4e86-8bab-833bcb2e7d80","order_by":1,"name":"Fubo Zhu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYBAC9gYeBgbGBgY5NvbmA8Rp4TkA0WLMx3MsgTQtifMkchSI1CKRe/Dhzx2H09sYchgYflRsI0ZLXrKB5JnDuW0MZw8w9py5TViLvUSOmYRhG1ALY18CM2MbEVp4QFoS2w6nszHzGJCg5WDb4QQ2NqK18LxLNmxsSzds42FLOEiUX3jYQSHWZi0vP//xwQc/KojQggIOkKh+FIyCUTAKRgEuAAA3DTi/G5OTwQAAAABJRU5ErkJggg==","orcid":"","institution":"Huaiyin Normal University","correspondingAuthor":true,"prefix":"","firstName":"Fubo","middleName":"","lastName":"Zhu","suffix":""}],"badges":[],"createdAt":"2025-03-19 02:38:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6257186/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6257186/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94459469,"identity":"ef8bcde2-bd1e-4477-b038-fd2a698747f0","added_by":"auto","created_at":"2025-10-27 14:53:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":253764,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscriptrevised.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6257186/v1_covered_69190358-0de0-4fe7-b677-6156fedda1d5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A BLMI-Based Framework for Robust Stabilization of Stochastic Hybrid Systems Under Dual-Mode Uncertainties","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Bilinear matrix inequalities (BLMIs), Robust stabilization, Stochastic hybrid sys- tems (SHSs), Uncertain transition rates, Markovian switching","lastPublishedDoi":"10.21203/rs.3.rs-6257186/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6257186/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study investigates the robust stabilization problem for linear stochastic hybrid systems (SHSs) characterized by dual uncertainties: parametric variations in system matrices and bounded uncertainties in Markovian transition rates. 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