Invertibility of an operator arising in the theory of the control of linear systems.
type: Item
instance of: scholarly article
title: Invertibility of an operator arising in the theory of the control of linear systems.
zbMATH Open document ID: 1045.93011
DOI: 10.1023/A:1010254808822
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Sufficient conditions for the existence of a bounded inverse operator for a linear operator in Hilbert space having a matrix representation of the form \[ F = \left( \begin{matrix} F_1 & 0 & F_2 \\ F_3 & -F_1^* & F_5 \\ -F_5^* & F_2^* & F_4 \end{matrix}\right) \] are obtained, where \(F_3, F_4 \) are nonnegative self-adjoint operators. It is shown that such operators appear, in particular, in the study of problems of optimal control of linear systems unresolved for the derivatives. The conditions obtained are not necessary for the invertibility of an arbitrary operator \(F\) of such form. A simple operator confirming this proposition is given. The invertibility conditions are used to prove the unique solvability of a certain two-point boundary-value problem that arises from conditions for optimal control.
reviewed by: A. M. Kovalev
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 1927743
zbMATH Keywords: invertibility of operators
zbMATH Keywords: optimal control of linear systems
zbMATH Keywords: Hilbert space
zbMATH Keywords: two-point boundary-value problem
zbMATH Keywords: sufficient conditions
author: G. A. Kurina
MaRDI profile type: Publication
full work available at URL: a:1010254808822
OpenAlex ID: W178035193
description: scientific article; zbMATH DE number 1927743