Admissibility of diagonal state-delayed systems with a one-dimensional input space

TL;DR

This paper studies the conditions under which a control operator is admissible in a diagonal, state-delayed system with scalar input, using Laplace and Hardy space techniques to establish sufficient criteria.

Contribution

It provides new sufficient conditions for infinite-time admissibility of control operators in diagonal state-delayed systems with scalar inputs, based on spectral properties.

Findings

Eigenvalues determine admissibility conditions

Control operator properties influence admissibility

Laplace and Hardy space methods are effective

Abstract

In this paper we investigate admissibility of the control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t-\tau)+Bu(t)$, where $A$ generates a diagonal semigroup and $u$ is a scalar input function. Our approach is based on the Laplace embedding between $L^2$ and the Hardy space. The sufficient conditions for infinite-time admissibility are stated in terms of eigenvalues of the generator and in terms of the control operator itself.