Approximate controllability of infinite dimensional systems of the n-th order

Jerzy Stefan Respondek

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 2, page 199-212
  • ISSN: 1641-876X

Abstract

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The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.

How to cite

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Jerzy Stefan Respondek. "Approximate controllability of infinite dimensional systems of the n-th order." International Journal of Applied Mathematics and Computer Science 18.2 (2008): 199-212. <http://eudml.org/doc/207877>.

@article{JerzyStefanRespondek2008,
abstract = {The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.},
author = {Jerzy Stefan Respondek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {inverse Vandermonde matrix; basic symmetrical polynomials; distributed parameter system; linear operators; controllability},
language = {eng},
number = {2},
pages = {199-212},
title = {Approximate controllability of infinite dimensional systems of the n-th order},
url = {http://eudml.org/doc/207877},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Jerzy Stefan Respondek
TI - Approximate controllability of infinite dimensional systems of the n-th order
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 2
SP - 199
EP - 212
AB - The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.
LA - eng
KW - inverse Vandermonde matrix; basic symmetrical polynomials; distributed parameter system; linear operators; controllability
UR - http://eudml.org/doc/207877
ER -

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