A Study on Observer Design for a Class of Nonlinear Systems using Lyapunov Stability

A Study on Observer Design for a Class of Nonlinear Systems using Lyapunov Stability | 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 Study on Observer Design for a Class of Nonlinear Systems using Lyapunov Stability Babak Taran, Behnam Taran This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3851342/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 research proposes a novel Lyapunov-based method for designing an observer for a class of nonlinear systems whose unmeasured states appear linearly in the state-space model, while the coefficients can be nonlinear functions of the measured states and time. In the other words equations can be express as a Linear Parameter-Varying (LPV) systems in which the parameter-dependent matrices depend on time and accessible variables. Many papers that deal with developing an observer for LPV systems assume that the variable parts are bounded for the feasibility of the design. By extending the conventional method which is used to estimate the state variables in linear systems, this study introduces an innovative scheme that has no limitations on the scheduling parameters. In the error equations, which quantify the discrepancy between the actual system and the estimated system, the matrices dependent on scheduling parameters can exhibit stable eigenvalues, provided that the observer gain matrix is selected appropriately. This matrix should be a continuous function. The stability of the eigenvalues implies that the observer can accurately estimate the state variables, as shown by using Lyapunov stability analysis. Mathematics Subject Classification 34D20 58E25 Observers Linear parameter-varying systems Lyapunov stability 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. 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-3851342","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266862545,"identity":"64ac1506-3e3f-4ff3-9386-18bd7887f05a","order_by":0,"name":"Babak Taran","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYBACewYeBsYGCJvxAZDg4SOkxbABrMUAxGYGkTxshLQYHEBoYZMAkwRtaT978OMMhj/y5u1nj1V+zbGTYWNgfvjoBh4t9jx5yZIbGAwM55zJS7stuy0Z6DA2Y+McvH7JMZB8wGDAOIMhx+y25DZmoBYeNml8WgzOvzH+CdRiP4P/jVmx5LZ6IrTcyDEDOSxxhkSOGePHbYcJazGc8S7NcoaBcfIMiTfG0ozbjvOwMRPwiz1/7uGbPRVytjP4cww//txWbc/P3vzwMT4tUOdBKGYeMElQORJg/EGK6lEwCkbBKBgxAAC67ENNKyiIbAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Zanjan","correspondingAuthor":true,"prefix":"","firstName":"Babak","middleName":"","lastName":"Taran","suffix":""},{"id":266862546,"identity":"46a7fd05-1010-4965-b538-77b4bf4e86a3","order_by":1,"name":"Behnam Taran","email":"","orcid":"","institution":"University of Bologna","correspondingAuthor":false,"prefix":"","firstName":"Behnam","middleName":"","lastName":"Taran","suffix":""}],"badges":[],"createdAt":"2024-01-10 19:59:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3851342/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3851342/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50023561,"identity":"7d25e03a-0d81-4774-8de5-3e87d4bef257","added_by":"auto","created_at":"2024-01-23 09:22:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":609057,"visible":true,"origin":"","legend":"","description":"","filename":"AStudyonObserverDesignforaClassofNonlinear....pdf","url":"https://assets-eu.researchsquare.com/files/rs-3851342/v1_covered_a55b9fbe-98eb-430f-993a-13a3688c5979.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Study on Observer Design for a Class of Nonlinear Systems using Lyapunov Stability","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":"Observers, Linear parameter-varying systems, Lyapunov stability","lastPublishedDoi":"10.21203/rs.3.rs-3851342/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3851342/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research proposes a novel Lyapunov-based method for designing an observer for a class of nonlinear systems whose unmeasured states appear linearly in the state-space model, while the coefficients can be nonlinear functions of the measured states and time. 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