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

International Journal of Applied Mathematics and Computer Science (2008)

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

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topJerzy 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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