New results on exponential stability for Markovian jumping neural networks with time-varying discrete and distributed delays

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Volumn 225, Issue 3, 2011, Pages 300-311

  Zhang, D ^a   Yu, L ^a  

^a ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

delay dependent; linear matrix inequality; Markovian jumping neural networks; mean square exponential stability

Indexed keywords

BELONG TO; DELAY-DEPENDENT; DISCRETE AND DISTRIBUTED DELAYS; DISCRETE DELAY; EXPONENTIAL STABILITY; LOWER AND UPPER BOUNDS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN; MEAN-SQUARE; NEW RESULTS; NUMERICAL EXAMPLE; TIME VARYING; DELAY DEPENDENT; MARKOVIAN JUMPING; MEAN SQUARE EXPONENTIAL STABILITY;

DELAY CONTROL SYSTEMS; EXPONENTIAL FUNCTIONS; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; STABILITY CRITERIA; TIME VARYING NETWORKS; TIME VARYING SYSTEMS; UNCERTAIN SYSTEMS; LINEAR MATRIX INEQUALITIES; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); STABILITY;

LINEAR MATRIX INEQUALITIES; STABILITY CRITERIA;

EID: 79953184669     PISSN: 09596518     EISSN: 20413041     Source Type: Journal    
DOI: 10.1243/09596518JSCE1144     Document Type: Article

References (16)

1. Cichoki, A. and Unbehauen, R. Neural networks for optimization and signal processing, 1993 (Wiley, Chichester, UK).
2. Haykin, S. Neural networks: A comprehensive foundation, 1998 (Prentice Hall, Englewood Cliffs, New Jersey, USA).
3. Wang, Z., Liu, Y., and Liu, X. On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A, 2005, 345(4-6), 299-308. (Pubitemid 41262382)
4. Park, J. H. Further result on asymptotic stability criterion of cellular neural networks with timevarying discrete and distributed delays. Appl. Math. Comput., 2006, 182(2), 1661-1666. (Pubitemid 44838866)
5. He, Y., Liu, G., Rees, D., and Wu, M. Stability analysis for neural networks with time-varying interval delay. IEEE Trans. Neural Network., 2007, 18(6), 1850-1854.
6. Li, H., Chen, B., Zhou, Q., and Fang, S. Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys. Lett. A, 2008, 372(19), 3385-3394.
7. Li, H., Chen, B., Zhou, Q., and Qian, W. Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern. B Cybern., 2009, 39(1), 94-102.
8. Wang, G., Chen, W., and Liu, Y. Delay-dependent global robust stability criterion for neural networks with neutral-type time-varying delays. Proc. IMechE, Part I: J. Systems and Control Engineering, 2010, 224(4), 321-327. DOI: 10.1243/09596518JSCE996.
9. Li, T., Luo, Q., Sun, C. Y., and Zhang, B. Y. Exponential stability of recurrent neural networks with time-varying discrete and distributed delays. Nonlinear Anal. R. World Applic., 2009, 10(4), 2581-2589.
10. Zhu, X. L. and Wang, Y. Y. Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays. Phys. Lett. A, 2009, 373(44), 4066-4072.
11. Ma, K. Y., Yu, L., and Zhang, W. A. Global exponential stability of cellular neural networks with time-varying discrete and distributed delays. Neurocomputing, 2009, 72(10-12), 2705-2709.
12. Li, H., Chen, B., Zhou, Q., and Lin, C. Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Phys. Lett. A, 2008, 372(30), 4996-5003.
13. Liu, H. Y., Zhao, L., Zhang, Z. X., and Ou, Y. Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays. Neurocomputing, 2009, 72(16-18), 3669-3674.
14. Wang, G. J., Cao, J. D., and Liang, J. L. Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters. Nonlinear Dyn., 2009, 57(1-2), 209-218.
15. Gu, K., Kharitonov, V., and Chen, J. Stability of time-delay systems, 2003 (Springer, Berlin).
16. Han, Q. L. A discrete delay decomposition approach to stability of linear retarded and neutral systems. Automatica, 2009, 45(2), 517-524.