{"title":"带有Lévy噪声的混合中立型随机时滞微分方程的H∞和时滞反馈渐近稳定性","authors":"Mohamed Rhaima;Lassaad Mchiri;A Ben Makhlouf","doi":"10.1093/imamci/dnad002","DOIUrl":null,"url":null,"abstract":"This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN \n<tex>$H_{\\infty }$</tex>\n and asymptotically stable in \n<tex>${\\mathbb{L}}^{p}$</tex>\n. We end up with a numerical example that corroborates our theoretical findings.","PeriodicalId":56128,"journal":{"name":"IMA Journal of Mathematical Control and Information","volume":"40 1","pages":"106-132"},"PeriodicalIF":1.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"H∞ and Asymptotic Stability via delay feedback for hybrid neutral stochastic delay differential equations with Lévy noise\",\"authors\":\"Mohamed Rhaima;Lassaad Mchiri;A Ben Makhlouf\",\"doi\":\"10.1093/imamci/dnad002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN \\n<tex>$H_{\\\\infty }$</tex>\\n and asymptotically stable in \\n<tex>${\\\\mathbb{L}}^{p}$</tex>\\n. We end up with a numerical example that corroborates our theoretical findings.\",\"PeriodicalId\":56128,\"journal\":{\"name\":\"IMA Journal of Mathematical Control and Information\",\"volume\":\"40 1\",\"pages\":\"106-132\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Mathematical Control and Information\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10078818/\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Mathematical Control and Information","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10078818/","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
H∞ and Asymptotic Stability via delay feedback for hybrid neutral stochastic delay differential equations with Lévy noise
This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN
$H_{\infty }$
and asymptotically stable in
${\mathbb{L}}^{p}$
. We end up with a numerical example that corroborates our theoretical findings.
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