Well-posedness and approximate controllability of neutral network systems

TL;DR

This paper investigates the approximate controllability of neutral type retarded network systems by reformulating them as boundary control systems and applying infinite-dimensional linear system theory to derive verifiable controllability conditions.

Contribution

It introduces a new framework for analyzing neutral network systems' controllability using boundary control reformulation and a rank condition for verification.

Findings

Derived necessary and sufficient controllability conditions.

Proposed a rank condition for easy verification.

Utilized feedback theory of regular linear systems.

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 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.