Delay-dependent stability of linear multi-step methods for linear neutral systems

Guang-Da Hu; Lizhen Shao

Kybernetika (2020)

  • Volume: 56, Issue: 3, page 543-558
  • ISSN: 0023-5954

Abstract

top
In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. Combining with Lagrange interpolation, linear multi-step methods can be applied to the neutral systems. Utilizing the argument principle, a sufficient condition is derived for linear multi-step methods with preserving delay-dependent stability. Numerical examples are given to illustrate the main results.

How to cite

top

Hu, Guang-Da, and Shao, Lizhen. "Delay-dependent stability of linear multi-step methods for linear neutral systems." Kybernetika 56.3 (2020): 543-558. <http://eudml.org/doc/297210>.

@article{Hu2020,
abstract = {In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. Combining with Lagrange interpolation, linear multi-step methods can be applied to the neutral systems. Utilizing the argument principle, a sufficient condition is derived for linear multi-step methods with preserving delay-dependent stability. Numerical examples are given to illustrate the main results.},
author = {Hu, Guang-Da, Shao, Lizhen},
journal = {Kybernetika},
keywords = {neutral systems with multiple delays; delay-dependent stability; linear multi-step method; Lagrange interpolation; argument principle},
language = {eng},
number = {3},
pages = {543-558},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Delay-dependent stability of linear multi-step methods for linear neutral systems},
url = {http://eudml.org/doc/297210},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Hu, Guang-Da
AU - Shao, Lizhen
TI - Delay-dependent stability of linear multi-step methods for linear neutral systems
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 3
SP - 543
EP - 558
AB - In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. Combining with Lagrange interpolation, linear multi-step methods can be applied to the neutral systems. Utilizing the argument principle, a sufficient condition is derived for linear multi-step methods with preserving delay-dependent stability. Numerical examples are given to illustrate the main results.
LA - eng
KW - neutral systems with multiple delays; delay-dependent stability; linear multi-step method; Lagrange interpolation; argument principle
UR - http://eudml.org/doc/297210
ER -

References

top
  1. Aleksandrov, A. Y., Hu, G. D., Zhabko, A. P., 10.1109/tac.2014.2299012, IEEE Trans. Automat. Control 59 (2014), 2209-2214. MR3245263DOI10.1109/tac.2014.2299012
  2. Bellen, A., Zennaro, M., 10.1093/acprof:oso/9780198506546.001.0001, Oxford University Press, Oxford 2003. MR1997488DOI10.1093/acprof:oso/9780198506546.001.0001
  3. Brown, J. W., Churchill, R. V., Complex Variables and Applications., McGraw-Hill Companies, Inc. and China Machine Press, Beijing 2004. MR0112948
  4. Fridman, E., 10.1007/978-3-319-09393-2, Birkhäuser, New York 2014. MR3237720DOI10.1007/978-3-319-09393-2
  5. Hale, J. K., Lunel, S. M. Verduyn, 10.1093/imamci/19.1_and_2.5, IMA J. Math. Control Inform. 19 (2002), 5-23. MR1899001DOI10.1093/imamci/19.1_and_2.5
  6. Han, Q. L., 10.1093/imamci/20.4.371, IMA J. Math. Control Inform. 20 (2003), 371-386. MR2028146DOI10.1093/imamci/20.4.371
  7. Hu, G. D., 10.14736/kyb-2018-4-0718, Kybernetika 54 (2018), 718-735. MR3863252DOI10.14736/kyb-2018-4-0718
  8. Hu, G. D., Cahlon, B., 10.1016/s0377-0427(98)00215-5, J. Compt. Appl. Math. 102 (1999), 221-234. MR1674027DOI10.1016/s0377-0427(98)00215-5
  9. Hu, G. D., Liu, M., 10.1109/tac.2007.894539, IEEE Trans. Automat. Control 52 (2007), 720-724. MR2310053DOI10.1109/tac.2007.894539
  10. Huang, C., Vandewalle, S., 10.1137/s1064827502409717, SIAM J. Scientific Computing 25 (2004), 1608-1632. MR2087328DOI10.1137/s1064827502409717
  11. Johnson, L. W., Riess, R. Dean, Arnold, J. T., Introduction to Linear Algebra., Prentice-Hall, Englewood Cliffs 2000. 
  12. Jury, E. I., Theory and Application of z -Transform Method., John Wiley and Sons, New York 1964. 
  13. Kim, A. V., Ivanov, A. V., 10.1016/s0378-4754(97)00117-1, Math. Comput. Simul. 45 (1998), 377-384. MR1622949DOI10.1016/s0378-4754(97)00117-1
  14. Kolmanovskii, V. B., Myshkis, A., 10.1007/978-94-017-1965-0, Kluwer Academic Publishers, Dordrecht 1999. MR1680144DOI10.1007/978-94-017-1965-0
  15. Lambert, J. D., Numerical Methods for Ordinary Differential Systems., John Wiley and Sons, New York 1999. MR1127425
  16. Lancaster, P., Tismenetsky, M., The Theory of Matrices with Applications., Academic Press, Orlando 1985. MR0792300
  17. Maset, S., 10.1007/s002110100266, Numer. Math. 90 (2002), 555-562. MR1884230DOI10.1007/s002110100266
  18. Medvedeva, I. V., Zhabko, A. P., 10.1016/j.automatica.2014.10.074, Automatica 51 (2015), 372-377. MR3284791DOI10.1016/j.automatica.2014.10.074
  19. Tian, H., Kuang, J., 10.1016/0377-0427(93)e0269-r, J. Comput. Appl. Math. 58 (1995), 171-181. MR1343634DOI10.1016/0377-0427(93)e0269-r
  20. Vyhlidal, T., Zitek, P., 10.1109/tac.2009.2029301, IEEE Trans. Automat. Control 54 (2009), 2430-2435. MR2562848DOI10.1109/tac.2009.2029301

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.