Stability criteria of linear neutral systems with distributed delays

Guang-Da Hu

Kybernetika (2011)

  • Volume: 47, Issue: 2, page 273-284
  • ISSN: 0023-5954

Abstract

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In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.

How to cite

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Hu, Guang-Da. "Stability criteria of linear neutral systems with distributed delays." Kybernetika 47.2 (2011): 273-284. <http://eudml.org/doc/197130>.

@article{Hu2011,
abstract = {In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.},
author = {Hu, Guang-Da},
journal = {Kybernetika},
keywords = {neutral systems; distributed delay; stability criteria; neutral systems; distributed delay; stability criteria; asymptotic stability; numerical examples},
language = {eng},
number = {2},
pages = {273-284},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability criteria of linear neutral systems with distributed delays},
url = {http://eudml.org/doc/197130},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Hu, Guang-Da
TI - Stability criteria of linear neutral systems with distributed delays
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 2
SP - 273
EP - 284
AB - In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. The results of this paper extend those in the literature. Numerical examples are given to illustrate the presented results.
LA - eng
KW - neutral systems; distributed delay; stability criteria; neutral systems; distributed delay; stability criteria; asymptotic stability; numerical examples
UR - http://eudml.org/doc/197130
ER -

References

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  6. Hu, G. Da, Mitsui, T., 10.1007/BF01739823, BIT 35 (1995), 504–515. (1995) Zbl0841.65062MR1431345DOI10.1007/BF01739823
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  8. Lancaster, P., The Theory of Matrices with Applications, Academic Press, Orlando 1985. (1985) MR0245579
  9. Li, H., Zhong, S., Li, H., 10.1016/j.cam.2006.01.016, J. Comput. Appl. Math. 200 (2007), 441–447. (2007) Zbl1112.34058MR2276843DOI10.1016/j.cam.2006.01.016
  10. Michiels, W., Niculescu, S., Stability and Stabilization of Time Delay Systems: An Eigenvalue Based Approach, SIAM, Philadelphia 2007. (2007) Zbl1140.93026MR2384531
  11. Park, J. H., 10.1016/S0377-0427(00)00583-5, J. Comput. Appl. Math. 136 (2001), 177–184. (2001) MR1855889DOI10.1016/S0377-0427(00)00583-5
  12. Vyhlídal, T., Zítek, P., 10.1109/TAC.2009.2029301, IEEE Trans. Automat. Control 54 (2009), 2430–2435. (2009) MR2562848DOI10.1109/TAC.2009.2029301

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