{"paper_id":"2c034baf-3d04-433d-b2c0-52006ddd6f71","body_text":"Mixed H2/H∞ Control of Multi-Delay Systems with Application to Mixed Vehicular Platoons | 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 Mixed H 2 /H ∞ Control of Multi-Delay Systems with Application to Mixed Vehicular Platoons Qingfeng Shi, Qiyi Wang, Li Peng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9637588/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 paper investigates a multi-objective robust control problem for a class of continuous-time systems with multiple discrete time delays. To exploit heterogeneous historical state information, a memorybased state-feedback strategy is developed. Based on Lyapunov–Krasovskii stability theory, tractable delay-dependent synthesis conditions are derived in terms of linear matrix inequalities. A unified mixed H2/H∞ framework is further established to balance transient performance and robustness, where theH2 metric minimizes quadratic energy and theH∞ metric ensures attenuation of worst-case disturbances. The proposed framework is specialized to connected cruise control in mixed traffic platoons, where heterogeneous human reaction delays naturally lead to multiple time-delay dynamics. Time-domain simulations show that the resulting controller guarantees asymptotic stability, achieves enhanced transient performance with attenuated velocity fluctuations, and effectively suppresses traffic shockwave propagation under uncertainties. Systems Engineering Lyapunov-Krasovskii theory Linear matrix inequalities Mixed H2/H∞ control Time-delay systems Connected automated vehicle Full Text Additional Declarations The authors declare no competing interests. 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. 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-9637588\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":635913246,\"identity\":\"7337c432-27a0-4647-a360-329a0cd685ed\",\"order_by\":0,\"name\":\"Qingfeng Shi\",\"email\":\"\",\"orcid\":\"https://orcid.org/0009-0002-6285-7854\",\"institution\":\"Jiangnan University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Qingfeng\",\"middleName\":\"\",\"lastName\":\"Shi\",\"suffix\":\"\"},{\"id\":635913247,\"identity\":\"eadbb4b1-8d78-49c8-89d8-e633705b196c\",\"order_by\":1,\"name\":\"Qiyi Wang\",\"email\":\"\",\"orcid\":\"https://orcid.org/0000-0003-0137-2116\",\"institution\":\"Wuxi University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Qiyi\",\"middleName\":\"\",\"lastName\":\"Wang\",\"suffix\":\"\"},{\"id\":635913248,\"identity\":\"2e2a275a-44ae-4cef-9a32-b7b99063f2e8\",\"order_by\":2,\"name\":\"Li Peng\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYLCCBwY2zGwIbgIRWhIM0kjWwnAYlYsXmLP3Hn6RUHCenY/97OHXBTV3GPjZcwwYfu7ArcWy51yaRYLBbWY2nrw06xnHnjFI9rwxYOw9g1uLwY0cMwOwFoYcM2MetsMgEQNmxjY8Wu6/AWk5x8zG/wao5d9hBnuCWm7wGD9IMDjAzCaRY/yYtw1oiwQBLZY9OWbAQE4Ganljxszbd5hH4syzgoO9eLSYs58x/vDhj12yfH+O8Weeb4fl+NuTNz74ic9hDAxsEkA6mQHK4AGJHsCtAayF+QOQtmOAMkbBKBgFo2AUYAAAnKpLtTVqNNAAAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Jiangnan University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Li\",\"middleName\":\"\",\"lastName\":\"Peng\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-05-07 05:42:25\",\"currentVersionCode\":1,\"declarations\":{\"humanSubjects\":false,\"vertebrateSubjects\":false,\"conflictsOfInterestStatement\":false,\"humanSubjectEthicalGuidelines\":false,\"humanSubjectConsent\":false,\"humanSubjectClinicalTrial\":false,\"humanSubjectCaseReport\":false,\"vertebrateSubjectEthicalGuidelines\":false},\"doi\":\"10.21203/rs.3.rs-9637588/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-9637588/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":109019028,\"identity\":\"f892248a-10b3-4cc6-84ac-f0a2e3c5b3ff\",\"added_by\":\"auto\",\"created_at\":\"2026-05-11 18:26:36\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":510074,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"template.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9637588/v1_covered_fb0ae3d1-4dff-49c5-a503-3ab61c425c96.pdf\"}],\"financialInterests\":\"The authors declare no competing interests.\",\"formattedTitle\":\"\\u003cp\\u003eMixed \\u003cem\\u003eH\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003e2\\u003c/em\\u003e\\u003c/sub\\u003e\\u003cem\\u003e/H\\u003c/em\\u003e\\u003csub\\u003e∞\\u003c/sub\\u003e Control of Multi-Delay Systems with Application to Mixed Vehicular Platoons\\u003c/p\\u003e\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"Jiangnan University\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"Lyapunov-Krasovskii theory, Linear matrix inequalities, Mixed H2/H∞ control, Time-delay systems, Connected automated vehicle\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9637588/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9637588/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThis paper investigates a multi-objective robust control problem for a class of continuous-time systems with multiple discrete time delays. To exploit heterogeneous historical state information, a memorybased state-feedback strategy is developed. Based on Lyapunov–Krasovskii stability theory, tractable delay-dependent synthesis conditions are derived in terms of linear matrix inequalities. A unified mixed H2/H∞ framework is further established to balance transient performance and robustness, where theH2 metric minimizes quadratic energy and theH∞ metric ensures attenuation of worst-case disturbances. The proposed framework is specialized to connected cruise control in mixed traffic platoons, where heterogeneous human reaction delays naturally lead to multiple time-delay dynamics. Time-domain simulations show that the resulting controller guarantees asymptotic stability, achieves enhanced transient performance with attenuated velocity fluctuations, and effectively suppresses traffic shockwave propagation under uncertainties.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Mixed H2/H∞ Control of Multi-Delay Systems with Application to Mixed Vehicular Platoons\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-05-11 18:24:34\",\"doi\":\"10.21203/rs.3.rs-9637588/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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}}],\"origin\":\"\",\"ownerIdentity\":\"f74ffff4-2686-4b8e-b517-7e7e3828ff5a\",\"owner\":[],\"postedDate\":\"May 11th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":67939377,\"name\":\"Systems Engineering\"}],\"tags\":[],\"updatedAt\":\"2026-05-11T18:24:34+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-05-11 18:24:34\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-9637588\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-9637588\",\"identity\":\"rs-9637588\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}