Admissibility of Diagonal State-Delayed Systems with a One-Dimensional Input Space

摘要

In this paper we investigate admissibility of the control operator B in a Hilbert space state-delayed dynamical system setting of the form. z(t) = Az(t-t)+ Bu(t), where A generates a diagonal semigroup and u is a scalar input function. Our approach is based on the Laplace embedding between L2 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.