arXiv subjects

Radoslaw Zawiski

Publications and source records attributed to Radoslaw Zawiski.

5 recordsLinked to original sources

arXiv2022

Admissibility of retarded diagonal systems with one-dimensional input space

We investigate infinite-time admissibility of a control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t)+A_1 z(t-τ)+Bu(t)$, where $A$ generates a diagonal $C_0$-semigroup, $A_1\in\mathcal{L}(X)$ is also diagonal and $u\in L^2(0,\infty;\mathbb{C})$. Our approach is based on the Laplace embedding between $L^2$ and the Hardy space $H^2(\mathbb{C}_+)$. The results are expressed in terms of the eigenvalues of $A$ and $A_1$ and the sequence representing the control operator.

math.OC↗

arXiv2020

Laplace--Carleson embeddings on model spaces and boundedness of truncated Hankel and Toeplitz operators

A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case.

math.FA↗

arXiv2019

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

In this paper we investigate admissibility of the control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t-τ)+Bu(t)$, 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.

math.OC↗

arXiv2018

On the admissibility of retarded delay systems

We investigate a Hilbert space dynamical system of the form $\dot{z}(t)=Az(t)+A_1z(t-τ)+Bu(t)$, where $A$ generates a semigroup of contractions and $A_1$ is a bounded operator, in order to determine whether the operator $B$ is admissible. Our approach is based on the Miyadera--Voigt perturbation theorem and the Weiss conjecture on admissibility of control operators for contraction semigroups. We demonstrate that the retarded delay system can be represented as a well-posed abstract Cauchy problem with a solution formed by an initially log-concave bounded semigroup.

math.OC↗

arXiv2018

Exact controllability of non-Lipschitz semilinear systems

We present sufficient conditions for exact controllability of a semilinear infinite dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz continuous. Our main result is based on a fixed point type application of the Schmidt existence theorem and illustrated by a nonlinear transport partial differential equation.

math.FA↗