Well-posedness and approximate controllability of neutral network systems

Yassine El Gantouh; Said Hadd

doi:10.3934/nhm.2021018

Article Contents

2021, Volume 16, Issue 4: 569-589. Doi: 10.3934/nhm.2021018 open access

This issue Previous Article Bi-Continuous semigroups for flows on infinite networks Next Article Convex and quasiconvex functions in metric graphs

Well-posedness and approximate controllability of neutral network systems

Yassine El Gantouh and
Said Hadd^,

Department of Mathematics, Faculty of Sciences Agadir, Ibn Zohr University, Hay Dakhla, BP. 8106, 80000–Agadir, Morocco

^* Corresponding author: Said Hadd, s.hadd@uiz.ac.ma
^* Corresponding author: Said Hadd, s.hadd@uiz.ac.ma

Received: January 31, 2021

Revised: April 30, 2021

Early access: June 2021

Published: December 2021

This work has been supported by COST Action CA18232. The authors would like to thank Prof. A. Rhandi for discussing some part of this paper

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Abstract

In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the rich theory of infinite-dimensional linear systems to derive necessary and sufficient conditions for the approximate controllability. Moreover, we propose a rank condition for which we can easily verify the conditions of controllability. Our approach is mainly based on the feedback theory of regular linear systems in the Salamon-Weiss sense.

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Mathematics Subject Classification: Primary: 35F46, 93B05; Secondary: 93C20.

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