On the stability of neutral-type uncertain systems with multiple time delays

Pin-Lin Liu

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 2, page 221-229
  • ISSN: 1641-876X

Abstract

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The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.

How to cite

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Liu, Pin-Lin. "On the stability of neutral-type uncertain systems with multiple time delays." International Journal of Applied Mathematics and Computer Science 15.2 (2005): 221-229. <http://eudml.org/doc/207737>.

@article{Liu2005,
abstract = {The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.},
author = {Liu, Pin-Lin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Razumikhin-type theorem; neutral type uncertain systems; time-delay},
language = {eng},
number = {2},
pages = {221-229},
title = {On the stability of neutral-type uncertain systems with multiple time delays},
url = {http://eudml.org/doc/207737},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Liu, Pin-Lin
TI - On the stability of neutral-type uncertain systems with multiple time delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 2
SP - 221
EP - 229
AB - The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.
LA - eng
KW - Razumikhin-type theorem; neutral type uncertain systems; time-delay
UR - http://eudml.org/doc/207737
ER -

References

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  8. He P. and Cao D.Q. (2004): Algebraic stability criteria of linear neutral systems with multiple time delays. - Appl. Math. Comput., Vol. 68,No. 155, pp. 643-653. Zbl1060.34044
  9. He Y., Wu M., She J.H. and Liu G.P. (2004): Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. - Syst. Contr. Lett., Vol. 51, pp. 57-65. Zbl1157.93467
  10. Lien C.H. (1999): Asymptotic criterion for neutral systems with multiple time delays. - Elec. Lett., Vol. 35, pp. 850-852. 
  11. Lien C.H. and Fan K.K. (2000): Robust stability for a class of neutral time delay systems. - Proc. Automat. Contr. Conf., Hsinchu, Taiwan, pp. 576-580. 
  12. Mahmound M.S. (2000): Robust Control and Filtering for Time-Delay Systems. - New York: Marcel Dekker, Inc. 
  13. Niculescu S.I. (2001): Delay Effects in Stability, A Robust Stability Approach. - London: Springer. Zbl0997.93001
  14. Su T.J. and Huang C.G. (1992): Robust stability of delay dependence for linear uncertain systems. - IEEE Trans. Automat. Contr., Vol. AC-37, No. 10, pp. 1656-1659. Zbl0770.93077
  15. Yan J.T. (2000): Robust stability analysis of uncertain time delay systems with delay-dependence. - Elec. Lett., Vol. 37, No. 2, pp. 135-137. 
  16. Yang M.S. and Liu P.L. (2002): On asymptotic stability of linear neutral delay-differential systems. - Int. J. Syst. Sci., Vol. 33, No. 11, pp. 901-907. Zbl1035.93056

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