Analysis and control of integro-differential Volterra equations with delays

2021/02/17 by Younes ElKadiri, ElKadiri, Younes, Saïd Hadd +3
Engineering · Mathematics · #34K30 #45K05 #93C23 #93C25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2102.08805

openalex publication_date 2021/02/17 · openalex created_date 2023/08/22 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to introduce a semigroup approach to linear integro-differential systems with delays in state, control and observation parts. On the one hand, we use product spaces to reformulate state-delay integro-differential equations to a standard Cauchy problem and then use a perturbation technique (feedback) to prove the well-posendess of the problem, a new variation of constants formula for the solution as well as some spectral properties. On the other hand, we use the obtained results to prove that integro-differential systems with delays in state, control and observation parts form a subclass of distributed infinite-dimensional regular linear systems in the Salamon-Weiss sense.

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