$L^q$ approximate controllability frequency criterion for linear difference delay equations with distributed delays

TL;DR

This paper establishes a frequency domain criterion for $L^q$ approximate controllability of linear difference delay equations with distributed delays, providing a theoretical foundation for control analysis in such systems.

Contribution

It introduces a necessary and sufficient frequency domain criterion for $L^q$ approximate controllability and derives an upper bound for the minimal controllability time.

Findings

Criterion is necessary and sufficient for controllability

Provides an upper bound for minimal controllability time

Extends controllability analysis to systems with distributed delays

Abstract

Based on an algebraic point of view and the realization theory developed by Y. Yamamoto, the present paper states a necessary and sufficient criterion, given in the frequency domain, for the $L^q$ approximate controllability in finite time of linear difference delay equations with distributed delays. Furthermore, an upper bound for the minimal time of the $L^q$ approximate controllability is obtained.