Analysis and control of integro-differential Volterra equations with delays

We present a novel approach to address integro-differential systems incorporating state, input, and output delays. Our approach leverages product spaces and employs a boundary perturbation technique. Initially, we focus on state-delay equations, wherein we introduce a variation of constants formula...

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Bibliographic Details
Published in:Semigroup forum 2023-10, Vol.107 (2), p.375-401
Main Authors: El Kadiri, Youness, Hadd, Said, Bounit, Hamid
Format: Article
Language:English
Subjects:
Algebra
Delay
Differential equations
Eigenvalues
Eigenvectors
Equivalence
Mathematical analysis
Mathematics
Mathematics and Statistics
Perturbation methods
Research Article
Volterra integral equations
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Summary:We present a novel approach to address integro-differential systems incorporating state, input, and output delays. Our approach leverages product spaces and employs a boundary perturbation technique. Initially, we focus on state-delay equations, wherein we introduce a variation of constants formula for the mild solution. Additionally, we establish spectral properties using a characteristic equation. Subsequently, we extend our analysis to integro-differential systems affected by state, input, and output delays. Notably, we demonstrate the equivalence between a such delay system and a regular free-delay system within the Salamon–Weiss framework. This equivalence sheds valuable insights on the nature of the integro-differential system under consideration.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-023-10378-7