A bilinear optimization-based approach for eigenstructure assignment output feedback control of  second-order linear systems

A bilinear optimization-based approach for eigenstructure assignment output feedback control of second-order linear systems | 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 A bilinear optimization-based approach for eigenstructure assignment output feedback control of second-order linear systems José Mário Araújo, Eugenio de Bona Castelan, Carlos Eduardo Trabuco Dórea, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7376730/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Mar, 2026 Read the published version in Journal of Control, Automation and Electrical Systems → Version 1 posted 9 You are reading this latest preprint version Abstract In this paper, we propose an eigenstructure assignment approach for static-output feedback control design of second-order systems. First, the eigenvalue assignment problem is translated into that of solving coupled Sylvester equations, resulting in a set of bilinear matrix equalities, involving the corresponding left and right eigenvectors. These equalities are used as constraints of bilinear programming problems, for which different cost functions are proposed, representing the numerical conditioning of the solution and sensitivity functions, which serve as a measure of the robustness of the assigned eigenvalues against uncertainties in the system's parameters. The method can be extended to the design of a second-order dynamic output feedback compensator with a suitable number of degrees of freedom for cases where arbitrary eigenvalue assignment is not guaranteed with Kimura's condition or a less conservative one. Numerical examples using two benchmarks are presented to illustrate the effectiveness of the proposed approach. Second-order systems Output feedback Coupled-Sylvester equations Eigenstructure assignment Bilinear optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Mar, 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 11 Nov, 2025 Reviewers agreed at journal 26 Oct, 2025 Reviews received at journal 25 Sep, 2025 Reviewers agreed at journal 18 Sep, 2025 Reviewers invited by journal 12 Sep, 2025 Editor assigned by journal 19 Aug, 2025 Submission checks completed at journal 18 Aug, 2025 First submitted to journal 14 Aug, 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. 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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-7376730","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":501922659,"identity":"45aa3746-3125-4ba6-ae03-4a08a2f9d82e","order_by":0,"name":"José Mário Araújo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBACxgYQacAgx8Z8BsRiZmCQIFKLMRtbDpFaYCCxgWgtzO3diZ8rCmzS+9h4D35gqLBObJDufYDfYT1nN0ueMUjLbWPjS5ZgOJOe2CBz3AC/lhm5GyQbDA7ntsn3GEgwth1ObJBIw+8woJbNP4Fa0tnYeIx/MP4jTss2kC0JQC1mEowNxGjpObvNssEgzRDolzSLhGPpxm0yx/BrMWzv3Xyz4Y+NvHwb7+EbH2qsZful2whoaUDmJQAxG34NDAzyhBSMglEwCkbBKGAAAI0QQLnqCC79AAAAAElFTkSuQmCC","orcid":"","institution":"Bahia Federal Institute of Education, Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"José","middleName":"Mário","lastName":"Araújo","suffix":""},{"id":501922660,"identity":"3b942eaf-4363-43d5-9899-9f8c26902bc2","order_by":1,"name":"Eugenio de Bona Castelan","email":"","orcid":"","institution":"Universidade Federal de Santa Catarina","correspondingAuthor":false,"prefix":"","firstName":"Eugenio","middleName":"de Bona","lastName":"Castelan","suffix":""},{"id":501922661,"identity":"4d380bf3-9c00-4b04-8199-14096cdedf95","order_by":2,"name":"Carlos Eduardo Trabuco Dórea","email":"","orcid":"","institution":"Federal University of Rio Grande do Norte","correspondingAuthor":false,"prefix":"","firstName":"Carlos","middleName":"Eduardo Trabuco","lastName":"Dórea","suffix":""},{"id":501922662,"identity":"e57ef2e7-df3a-4b7d-a409-78875b9d6bfa","order_by":3,"name":"Isaac Dantas Isidório","email":"","orcid":"","institution":"Federal University of Rio Grande do Norte","correspondingAuthor":false,"prefix":"","firstName":"Isaac","middleName":"Dantas","lastName":"Isidório","suffix":""}],"badges":[],"createdAt":"2025-08-14 20:23:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7376730/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7376730/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40313-026-01273-x","type":"published","date":"2026-03-23T16:09:48+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":105754969,"identity":"22a12851-dc2b-4b60-8739-91447dce7178","added_by":"auto","created_at":"2026-03-30 16:23:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7878832,"visible":true,"origin":"","legend":"","description":"","filename":"JCAESFINAL.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7376730/v1_covered_80e1f7a5-9711-4bb6-b6da-4f822865abdd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A bilinear optimization-based approach for eigenstructure assignment output feedback control of second-order linear systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-control-automation-and-electrical-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcae","sideBox":"Learn more about [Journal of Control, Automation and Electrical Systems](https://link.springer.com/journal/40313)","snPcode":"40313","submissionUrl":"https://submission.springernature.com/new-submission/40313/3","title":"Journal of Control, Automation and Electrical Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Second-order systems, Output feedback, Coupled-Sylvester equations, Eigenstructure assignment, Bilinear optimization","lastPublishedDoi":"10.21203/rs.3.rs-7376730/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7376730/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we propose an eigenstructure assignment approach for static-output feedback control design of second-order systems. 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