Exponential dissipative control for conformable nonlineardynamical systems

Exponential dissipative control for conformable nonlineardynamical 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 Article Exponential dissipative control for conformable nonlineardynamical systems Slim Dhahri, Essia Ben Alaia, Hamdi Gassara This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8530851/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted 12 You are reading this latest preprint version Abstract This paper addresses the design of a controller that exponentially stabilizes Conformable Nonlinear Dynamical Systems (CNDSs) with time delay. To address the nonlinear dynamics of the system, we employ a Polynomial Fuzzy (PF) modeling approach. This method provides an exact representation of the original CNDS and serves as a generalized framework that extends the classical Takagi-Sugeno Fuzzy (TSF) model. The controller is designed to ensure not only exponential stability, which implies a prescribed convergence rate compared to asymptotic stability, but also the strictly $(\mathcal{U},\mathcal{V},\mathcal{W})$-$\sigma$-dissipativity of the closed-loop system. Moreover, the controller design explicitly accounts for partial state measurements by employing an observer to estimate the unmeasured states. The proposed conditions reduce conservatism for several reasons. A decoupling technique is employed that alleviates the limitations of the singular value decomposition approach, as the Lyapunov matrix is not restricted to a specific structure. In addition, the decision variables, essentially the controller gains, are not constant but are allowed to be polynomial functions, computed using the SOSTOOLS framework rather than the standard LMI toolbox. Furthermore, recently proposed relaxed conditions for parameterized Linear Matrix Inequalities (LMIs) in double-sum form are extended to parameterized Sum-of-Squares (SOS) constraints. The effectiveness of the proposed results is shown through a numerical example. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Conformable fractional-order derivative SOS approach exponential stability analysis observer design Polynomial fuzzy model Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 30 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 20 Jan, 2026 Reviews received at journal 16 Jan, 2026 Reviews received at journal 15 Jan, 2026 Reviews received at journal 15 Jan, 2026 Reviewers agreed at journal 15 Jan, 2026 Reviewers agreed at journal 15 Jan, 2026 Reviewers agreed at journal 14 Jan, 2026 Reviewers invited by journal 14 Jan, 2026 Editor assigned by journal 12 Jan, 2026 Editor invited by journal 12 Jan, 2026 Submission checks completed at journal 08 Jan, 2026 First submitted to journal 08 Jan, 2026 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. 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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-8530851","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":575578852,"identity":"9342d917-42bf-48d2-b618-04be15fbb5c6","order_by":0,"name":"Slim Dhahri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYFCCHAZmBgYJOcYGIJuHFC3GJGthSATpIE6LfHvuwc+FeyzSm2ckMD5428Zgz99AQIvBmXfJ0jOeSeQ2zkhgNpzbxpA44wAhLRI5BtI8B8Ba2KR52xgSGAhpkZ+RY/wbqCWdcUYC+2+gFnt5QloYbuSYgWxJAGphYwZqYdxA0GFn3phZA7UYNvY8bJacc04icSNBh7XnGN/mOVAnb9iefPDDmzIbezmCDoMBwwZwZEoQqx5kHQlqR8EoGAWjYIQBAKNfPIP8gQ98AAAAAElFTkSuQmCC","orcid":"","institution":"Al Jouf University","correspondingAuthor":true,"prefix":"","firstName":"Slim","middleName":"","lastName":"Dhahri","suffix":""},{"id":575578853,"identity":"8eefae8f-2305-43a8-9cd1-5fc4a23a8222","order_by":1,"name":"Essia Ben Alaia","email":"","orcid":"","institution":"Al Jouf University","correspondingAuthor":false,"prefix":"","firstName":"Essia","middleName":"Ben","lastName":"Alaia","suffix":""},{"id":575578854,"identity":"63ddc5fd-6813-4b59-a326-d82f3e6ffbcb","order_by":2,"name":"Hamdi Gassara","email":"","orcid":"","institution":"University of Sfax","correspondingAuthor":false,"prefix":"","firstName":"Hamdi","middleName":"","lastName":"Gassara","suffix":""}],"badges":[],"createdAt":"2026-01-06 11:39:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8530851/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8530851/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-44606-1","type":"published","date":"2026-04-30T15:58:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100621846,"identity":"30c3962e-c3a6-4ae3-ac87-6348cd7734c0","added_by":"auto","created_at":"2026-01-19 18:35:53","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5455,"visible":true,"origin":"","legend":"","description":"","filename":"a405d591e5114bd7b1c1ad4d15f89eed.json","url":"https://assets-eu.researchsquare.com/files/rs-8530851/v1/87bdf24a2dda497178ec627a.json"},{"id":108437676,"identity":"7b939792-7029-4c5f-bc8e-e098fc752d20","added_by":"auto","created_at":"2026-05-04 16:01:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":286048,"visible":true,"origin":"","legend":"","description":"","filename":"Scientificreport.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8530851/v1_covered_22ace527-9b0f-4d32-92fb-b22b5301859f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exponential dissipative control for conformable nonlineardynamical systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Conformable fractional-order derivative, SOS approach, exponential stability analysis, observer design, Polynomial fuzzy model","lastPublishedDoi":"10.21203/rs.3.rs-8530851/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8530851/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper addresses the design of a controller that exponentially stabilizes Conformable Nonlinear Dynamical Systems (CNDSs) with time delay. To address the nonlinear dynamics of the system, we employ a Polynomial Fuzzy (PF) modeling approach. This method provides an exact representation of the original CNDS and serves as a generalized framework that extends the classical Takagi-Sugeno Fuzzy (TSF) model. The controller is designed to ensure not only exponential stability, which implies a prescribed convergence rate compared to asymptotic stability, but also the strictly $(\\mathcal{U},\\mathcal{V},\\mathcal{W})$-$\\sigma$-dissipativity of the closed-loop system. Moreover, the controller design explicitly accounts for partial state measurements by employing an observer to estimate the unmeasured states. The proposed conditions reduce conservatism for several reasons. A decoupling technique is employed that alleviates the limitations of the singular value decomposition approach, as the Lyapunov matrix is not restricted to a specific structure. 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