ArticlesNo Access

ROBUST EXPONENTIAL STABILITY OF MARKOVIAN JUMPING NEURAL NETWORKS WITH TIME-VARYING DELAY

College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Road, Wuxi, Jiangsu 214122, P. R. China

Search for more papers by this author

XUYANG LOU

College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Road, Wuxi, Jiangsu 214122, P. R. China

CSIRO Division of Mathematical and Information Sciences, Waite Road, Urrbrae, SA 5064, Australia

Search for more papers by this author

and

BAOTONG CUI

College of Communication and Control Engineering, Jiangnan University, 1800 Lihu Road, Wuxi, Jiangsu 214122, P. R. China

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0129065708001531Cited by:13

Abstract

This paper considers the robust stability of a class of neural networks with Markovian jumping parameters and time-varying delay. By employing a new Lyapunov–Krasovskii functional, a sufficient condition for the global exponential stability of the delayed Markovian jumping neural networks is established. The proposed condition is also extended to the uncertain cases, which are shown to be the improvement and extension of the existing ones. Finally, the validity of the results are illustrated by an example.

Keywords:

References

S. Arik, IEEE Trans. Circuits Syst. I 47(7), 1089 (2000), DOI: 10.1109/81.855465. Crossref, Google Scholar
J. D. Cao and J. Wang, IEEE Trans. Circuits Syst. I 52(5), 920 (2005). Google Scholar
T. P. Chen and L. B. Rong, Physics Letter A 317, 436 (2003), DOI: 10.1016/j.physleta.2003.08.066. Crossref, ISI, Google Scholar
Y. R. Liu, Z. D. Wang and X. H. Liu, Neural Networks 19, 667 (2006), DOI: 10.1016/j.neunet.2005.03.015. Crossref, Medline, ISI, Google Scholar
Z. G. Zeng and J. Wang, IEEE Trans. Neural Networks 17(3), 623 (2006), DOI: 10.1109/TNN.2006.873283. Crossref, Medline, ISI, Google Scholar
T. Ensari and S. Arik, IEEE Trans. Circuits Syst. II 52(3), 126 (2005), DOI: 10.1109/TCSII.2004.842050. Crossref, Google Scholar
X. Y. Lou and B. T. Cui, Neurocomputing 69, 2374 (2006), DOI: 10.1016/j.neucom.2006.02.019. Crossref, ISI, Google Scholar
W. Wu, B. T. Cui and X. Y. Lou, Neurocomputing 70, 1085 (2007). Crossref, ISI, Google Scholar
H. T. Lu, R. M. Shen and F. L. Chung, IEEE Trans. Neural Networks 16(6), 1694 (2005), DOI: 10.1109/TNN.2005.853336. Crossref, Medline, ISI, Google Scholar
S. Arik, Neural Networks 17, 1027 (2004), DOI: 10.1016/j.neunet.2004.02.001. Crossref, Medline, ISI, Google Scholar
Y. He, M. Wu and J. H. She, IEEE Trans. Circuits Syst. II 53(7), 553 (2006), DOI: 10.1109/TCSII.2006.883209. Google Scholar
K. Yuan, J. D. Cao and H. X. Li, IEEE Trans. Syst. Man Cybern.-Part B 36(6), 1356 (2006), DOI: 10.1109/TSMCB.2006.876819. Crossref, Medline, ISI, Google Scholar
L. B. Rong, Physics Letters A 339, 63 (2005), DOI: 10.1016/j.physleta.2005.03.023. Crossref, ISI, Google Scholar
J. D. Cao and J. Wang, IEEE Trans. Circuits Syst. I 52(2), 417 (2005). Google Scholar
Z. Zuo and Y. Wang, IET Control Theory Appl. 1(1), 387 (2007), DOI: 10.1049/iet-cta:20060056. Crossref, ISI, Google Scholar
S. Y. Xuet al., IEEE Trans. Syst. Man Cybern. 35(6), 1317 (2005). Crossref, ISI, Google Scholar
V. Singh, IEE Proc. Control Theory Appl. 151(1), 125 (2004), DOI: 10.1049/ip-cta:20040091. Crossref, Google Scholar
N. Ozcan and S. Arik, IEEE Trans. Circuits Syst. I 53(1), 166 (2006), DOI: 10.1109/TCSI.2005.855724. Crossref, Google Scholar
X. Y. Lou and B. T. Cui, Neurocomputing 70, 273 (2006), DOI: 10.1016/j.neucom.2006.02.020. Crossref, ISI, Google Scholar
C. D. Li and X. F. Liao, IEEE Trans. Circuits Syst. II 53(9), 901 (2006), DOI: 10.1109/TCSII.2006.880335. Crossref, Google Scholar
Z. D. Wanget al., Chaos, Solitons and Fractals 32, 62 (2007), DOI: 10.1016/j.chaos.2005.10.061. Crossref, ISI, Google Scholar
X. Mao, IEEE Trans. Autom. Control 47(10), 1604 (2002). ISI, Google Scholar
Z. Shu, J. Lam and S. Y. Xu, Automatica 42, 2001 (2006), DOI: 10.1016/j.automatica.2006.06.016. Crossref, ISI, Google Scholar
X. Y. Lou and B. T. Cui, J. Math. Anal. Appl. 328(1), 316 (2007), DOI: 10.1016/j.jmaa.2006.05.041. Crossref, ISI, Google Scholar
Z. D. Wanget al., Physics Letters A 356, 346 (2006), DOI: 10.1016/j.physleta.2006.03.078. Crossref, ISI, Google Scholar
X. Y. Lou and B. T. Cui, IEEE Trans. Trans. Syst. Man Cybern.-Part B 37(3), 713 (2007), DOI: 10.1109/TSMCB.2006.887426. Crossref, Medline, ISI, Google Scholar
D. Yue and Q. L. Han, IEEE Trans. Automatic Control 50(2), 217 (2005). ISI, Google Scholar
M. Mariton , Jump Linear Control Systems ( Marcel-Dekker , New York , 1990 ) . Google Scholar
H. J. Kushner , Stochastic Stability and Control ( Academic Press , New York , 1967 ) . Google Scholar
A. V. Skorokhod , Asymptotic Methods in the Theory of Stochastic Differential Equations ( American Mathematical Society , Providence, RI , 1989 ) . Google Scholar
K. Gu , V. Kharitonov and J. Chen , Stability of Time-Delay Systems ( Birkhauser , Boston, MA , 2003 ) . Crossref, Google Scholar
L. Xie, Int. J. Control 63(4), 741 (1996), DOI: 10.1080/00207179608921866. Crossref, ISI, Google Scholar
S. Boyd et al. , Linear Matrix Inequalities in System and Control Theory ( SIAM , Philadephia, PA , 1994 ) . Crossref, Google Scholar

Vol. 18, No. 03

Metrics

Downloaded 31 times

History

Keywords

PDF download

System Upgrade on Mon, Jun 21st, 2021 at 1am (EDT)

ROBUST EXPONENTIAL STABILITY OF MARKOVIAN JUMPING NEURAL NETWORKS WITH TIME-VARYING DELAY

Abstract

References

Recommended