<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems and control theory where Sylvester equations widely appear, and for this reason we intend to give a mathematically rigorous introduction to the subject which is tailored to researchers and postgraduate students working on systems and control. This goal motivates the assumptions under which the results are developed. As an important example of applications we study the problem of designing an asymptotic state observer for a linear infinite-dimensional control system with a bounded input operator and an unbounded output operator.</p></abstract>

This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems and control theory where Sylvester equations widely appear, and for this reason we intend to give a mathematically rigorous introduction to the subject which is tailored to researchers and postgraduate students working on systems and control. This goal motivates the assumptions under which the results are developed. As an important example of applications we study the problem of designing an asymptotic state observer for a linear infinite-dimensional control system with a bounded input operator and an unbounded output operator.

Infinite-dimensional Sylvester equations: Basic theory and application to observer design

Department of Control and Measurements, West Pomeranian University of Technology, Gen. Sikorskiego 37, 70-313 Szczecin, Poland

International Journal of Applied Mathematics and Computer Science

This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the...

Infinite-dimensional Sylvester equations: Basic theory and application to observer design

Published Online: Jun 28, 2012

Page range: 245 - 257

DOI: https://doi.org/10.2478/v10006-012-0018-5

Keywords
infinite-dimensional Sylvester equation, implemented semigroup, state observer design

This content is open access.

Infinite-dimensional Sylvester equations: Basic theory and application to observer design

Published Online: Jun 28, 2012

Page range: 245 - 257

DOI: https://doi.org/10.2478/v10006-012-0018-5

Keywordsinfinite-dimensional Sylvester equation, implemented semigroup, state observer design

This content is open access.

Keywords
infinite-dimensional Sylvester equation, implemented semigroup, state observer design