Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method

Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method | 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 Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method Liangliang Li, Zhengwen Tu, Guanghui Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-796093/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 studies the problem for a class of state constrained impulsive nonlinear systems. Firstly, we establish two sufficient conditions for the stability of invariant sets of state constrained hybrid systems. Secondly, we construct the symmetric and asymmetric barrier Lyapunov functions, respectively. A feedback method is presented to solve the stabilization problem of constrained hybrid systems. Introduce the auxiliary matrix, combining with inductive method and linear matrix inequality theory, some sufficient conditions are obtained to ensure stability for state constrained hybrid dynamical networks by the attractive ellipsoid method approach. Finally, one example with simulations is given to validate the effectiveness of the proposed criteria. Electrical Engineering Mechanical Engineering Ocean Engineering Applied Mathematics State constrained Impulsive systems Barrier Lyapunov functions Nonlinear systems Stability Full Text 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-796093","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":45339600,"identity":"da37774e-7b20-4033-9fb1-e7e170e8708e","order_by":0,"name":"Liangliang Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYBACPmbmhgNAWoYNxHtQYCHHxt58AK8WNmZGsBYesJYEAwljPp5jCfi1MDA2gGgeBqiWxHkSOQr4tbAzNh74uaOWh4/97OEXQC3pbQw5DAw/KrbhddjB3jPHedh48tIsgFpy2xjOHmDsOXMbv194244B/ZJjZgDWwtiXwMzYhl/Lwb8gLfxvwFrS2Zh5DAhqOczbVsPDJpFj/ACoJYGNjRgtsm0HgFremIFCzLCNhy3hID6/8PMfPvzxbVudnHx/jvGHDxU28vLzHx988KMCtxYoOAy2UQLGPUBIPRDUgQjmD0SoHAWjYBSMghEIACBXTuRX3wGaAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2534-4286","institution":"Huaibei Normal University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Liangliang","middleName":"","lastName":"Li","suffix":""},{"id":45339601,"identity":"ae0ad152-4771-45cb-91cc-37ce772acb3e","order_by":1,"name":"Zhengwen Tu","email":"","orcid":"","institution":"Chongqing Three Gorges University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhengwen","middleName":"","lastName":"Tu","suffix":""},{"id":45339602,"identity":"904c8eeb-3619-43b3-b06c-dc9b2381089a","order_by":2,"name":"Guanghui Zhou","email":"","orcid":"","institution":"Huaibei Normal University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Guanghui","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2021-08-09 08:57:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-796093/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-796093/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":13667824,"identity":"0befe718-0d9e-45b8-ae67-e1cbf04b9443","added_by":"auto","created_at":"2021-09-17 10:54:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":528637,"visible":true,"origin":"","legend":"","description":"","filename":"nd202100809.pdf","url":"https://assets-eu.researchsquare.com/files/rs-796093/v1_covered.pdf"},{"id":12423804,"identity":"3be5ea60-e9e2-478c-ba02-1f2838260065","added_by":"auto","created_at":"2021-08-13 21:28:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":525075,"visible":true,"origin":"","legend":"","description":"","filename":"nd202100809.pdf","url":"https://assets-eu.researchsquare.com/files/rs-796093/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eStability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-796093/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"State constrained, Impulsive systems, Barrier Lyapunov functions, Nonlinear systems, Stability","lastPublishedDoi":"10.21203/rs.3.rs-796093/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-796093/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper studies the problem for a class of state constrained impulsive nonlinear systems. 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