Feedback Stabilization of Delayed Bilinear Systems

In this paper, we discuss the problem of feedback stabilization for distributed bilinear systems with discrete delay evolving on a Hilbert state space. Firstly, we prove the existence and uniqueness of the mild solution of system at hand. Secondly, we study the weak and strong stabilization. More pr...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 32; no. 1; pp. 87 - 100
Main Authors Hamidi, Z., Elazzouzi, A, Ouzahra, M.
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2024
Springer Nature B.V
Subjects
Computer Science
Engineering
Feedback
Mathematics
Mathematics and Statistics
Original Research
Stabilization
Thermodynamics
Time delay
Decay estimate
Bilinear systems
Feedback stabilization
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Summary:In this paper, we discuss the problem of feedback stabilization for distributed bilinear systems with discrete delay evolving on a Hilbert state space. Firstly, we prove the existence and uniqueness of the mild solution of system at hand. Secondly, we study the weak and strong stabilization. More precisely, we provide some sufficient conditions to ensure the weak and strong stabilization for the delayed bilinear system. Moreover, in the case of the strong stabilization, an explicit decay estimate is established. Applications to wave and heat equations with delayed bilinear parts are considered.
Bibliography:ObjectType-Article-1
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-021-00560-0