Controllability of linear impulsive systems – an eigenvalue approach

Vijayakumar S. Muni; Raju K. George

Kybernetika (2020)

  • Volume: 56, Issue: 4, page 727-752
  • ISSN: 0023-5954

Abstract

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This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.

How to cite

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S. Muni, Vijayakumar, and K. George, Raju. "Controllability of linear impulsive systems – an eigenvalue approach." Kybernetika 56.4 (2020): 727-752. <http://eudml.org/doc/297035>.

@article{S2020,
abstract = {This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.},
author = {S. Muni, Vijayakumar, K. George, Raju},
journal = {Kybernetika},
keywords = {eigenvalues; impulses; controllability},
language = {eng},
number = {4},
pages = {727-752},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Controllability of linear impulsive systems – an eigenvalue approach},
url = {http://eudml.org/doc/297035},
volume = {56},
year = {2020},
}

TY - JOUR
AU - S. Muni, Vijayakumar
AU - K. George, Raju
TI - Controllability of linear impulsive systems – an eigenvalue approach
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 4
SP - 727
EP - 752
AB - This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.
LA - eng
KW - eigenvalues; impulses; controllability
UR - http://eudml.org/doc/297035
ER -

References

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  8. Muni, V. S., George, R. K., , IMA J. Math. Control & Inform. 36(3) (2019), 869-899. MR4009506DOI
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  10. Xie, G., Wang, L., , J. Math. Anal. Appl. 304(1) (2005), 336-355. MR2124666DOI
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