Stability of perturbed delay homogeneous systems depending on a parameter

Ines Ben Rzig; Thouraya Kharrat

Kybernetika (2021)

  • Issue: 1, page 141-159
  • ISSN: 0023-5954

Abstract

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In this paper, we analyze the stability of homogeneous delay systems based on the Lyapunov Razumikhin function in the presence of a varying parameter. In addition, we show the stability of perturbed time delay systems when the nominal part is homogeneous.

How to cite

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Ben Rzig, Ines, and Kharrat, Thouraya. "Stability of perturbed delay homogeneous systems depending on a parameter." Kybernetika (2021): 141-159. <http://eudml.org/doc/297593>.

@article{BenRzig2021,
abstract = {In this paper, we analyze the stability of homogeneous delay systems based on the Lyapunov Razumikhin function in the presence of a varying parameter. In addition, we show the stability of perturbed time delay systems when the nominal part is homogeneous.},
author = {Ben Rzig, Ines, Kharrat, Thouraya},
journal = {Kybernetika},
keywords = {nonlinear homogeneous system; varying delay; stability; Lyapunov Razumikhin function},
language = {eng},
number = {1},
pages = {141-159},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability of perturbed delay homogeneous systems depending on a parameter},
url = {http://eudml.org/doc/297593},
year = {2021},
}

TY - JOUR
AU - Ben Rzig, Ines
AU - Kharrat, Thouraya
TI - Stability of perturbed delay homogeneous systems depending on a parameter
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
IS - 1
SP - 141
EP - 159
AB - In this paper, we analyze the stability of homogeneous delay systems based on the Lyapunov Razumikhin function in the presence of a varying parameter. In addition, we show the stability of perturbed time delay systems when the nominal part is homogeneous.
LA - eng
KW - nonlinear homogeneous system; varying delay; stability; Lyapunov Razumikhin function
UR - http://eudml.org/doc/297593
ER -

References

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  1. Aleksandrov, A. Yu., Zhabko, A. .P., , Appl. Math. Lett. 34 (2014), 43-50. MR3212227DOI
  2. Bacciotti, A., Rosier, L., Lyapunov Functions and Stability in Control Theory., Springer 2005. MR2146587
  3. Cao, Y., Samidurai, R., Sriraman, R., , J. Artif. Intell. Soft Comput. Res. 9 (2019), 3, 189-204. DOI
  4. Efimov, D., Perruquetti, W., Richard, J. P., , SIAM J. Control Optim. 52 (2014), 3, 1547-1566. MR3200418DOI
  5. Gu, K., Kharitonov, V. L., Chen, J., Stability of Time-Delay Systems., Birkhauser, Boston 2003. MR3075002
  6. Hale, J. K., Verduyn, L. S. M., Introduction to Functional-Differential Equations., Springer-Verlag, New York 1993. MR1243878
  7. Hermes, H., , J. Different. Equations 92 (1991), 1, 76-89. MR1113589DOI
  8. Hermes, H., Homogeneous coordinates and continuous asymptotically stabilizing feedback controls., Differential Equations Stability Control 109 (1991), 1, 249-260. MR1096761
  9. Hu, H., Yuan, X., Huang, L., Huang, C., , Math. Biosciences Engrg. 16 (2019), 5729-5749. MR4032648DOI
  10. Huang, C., Cao, J., Wen, F., Yang, X., , Plo One 08 (2016), 11, e0158813. DOI
  11. Huang, C., Qiao, Y., Huang, L., Agarwal, R., , Adv. Difference Equations 186 (2018), 12. MR3803384DOI
  12. Huang, C., Yang, Z., Yi, T., Zou, X., , J. Differential Equations 256 (2014), 2101-2114. MR3160438DOI
  13. Huang, C., Zhang, H., Cao, J., Hu, H., , Int. J. Bifurcation Chaos 29 (2019), 7, 1950091-23. MR3981039DOI
  14. Kawski, M., Homogeneous stabilizing feedback laws., Control Theory Advanced Technol. 6 (1990), 4, 497-516. MR1092775
  15. Khalil, K. H., Nonlinear Systems. (Third edition), Prentice-Hall, Upper Saddle River, NJ 2002. 
  16. Krasovskii, N. N., Stability of Motion. Applications of Lyapunov's Second Method to Differential Systems and Equations with Delay., Stanford University Press, Stanford 1963. MR0147744
  17. Lin, Y., Sontag, E. D., Wang, Y., , Int. J. Robust Nonlinear Control 5 (1995), 3, 187-205. MR1329624DOI
  18. Long, X., S.Gong, , Appl. Math. Lett. 100 (2019), 9, 106027. MR4008616DOI
  19. Massera, J. L., 10.2307/1969955, Ann. Math.Second Series 64 (1958), 7, 182-206. MR0079179DOI10.2307/1969955
  20. Raja, R., Karthik Raja, U., Samidurai, R., Leelamani, A., , J. Franklin Inst. 350 (2013), 10, 3217-3247. MR3123415DOI
  21. Razumikhin, B. S., The application of Lyapunov's method to problems in the stability of systems with delay., Automat. Remote Control 21 (1960), 515-520. MR0118639
  22. Rosier, L., , Systems Control Lett. 19 (1992), 6, 467-473. MR1195304DOI
  23. Sepulchre, R., Aeyels, D., , Math. Control Signals Systems 9 (1996), 3, 34-58. MR1410047DOI
  24. Zubov, V. I., Mathematical Methods for the Study of Automatic Control Systems., Pergamon Press, New York - Oxford - London - Paris; Jerusalem Academic Press, Jerusalem 1962. MR0151695

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