Mean square exponential stability for uncertain delayed stochastic neural networks with markovian jump parameters

Circuits, Systems, and Signal Processing

Volumn 29, Issue 2, 2010, Pages 331-348

  Zhou, Qi ^a   Chen, Bing ^b   Lin, Chong ^b   Li, Hongyi ^c  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b QINGDAO UNIVERSITY   (China)

^c HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

LMIs; Markovian jump parameters; Neural networks; Stochastic systems; Time varying delays

Indexed keywords

DELAY-DEPENDENT; DELAY-DEPENDENT STABILITY CONDITION; LMIS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMP PARAMETERS; MEAN SQUARE EXPONENTIAL STABILITY; NUMERICAL EXAMPLE; STABILITY CONDITION; STOCHASTIC NEURAL NETWORK; TIME-VARYING DELAY;

EXPONENTIAL FUNCTIONS; FUZZY CONTROL; HOPFIELD NEURAL NETWORKS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STOCHASTIC SYSTEMS; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

NEURAL NETWORKS;

EID: 77954565303     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-009-9138-z     Document Type: Article

References (24)

1. W. Chen, X. Lu, Mean square exponential stability of uncertain stochastic delayed neural networks. Phys. Lett. A 372, 1061-1069 (2007)
2. Y. He, M. Wu, J.-H. She, G.-P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51, 57-65 (2004)
3. Y. He, M. Wu, J.-H. She, G.-P. Liu, Parameter-dependent Lyapunov functional for stability of timedelay systems with polytopic-type uncertainties. IEEE Trans. Automat. Contr. 49, 828-832 (2004)
4. H. Huang, G. Feng, Delay-dependent stability for uncertain stochastic neural networks with timevarying delay. Physica A 381, 93-103 (2007) (Pubitemid 46829678)
5. H. Huang, D. W. C. Ho, Y. Qu, Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw. 20, 799-809 (2007)
6. H. Li, B. Chen, Q. Zhou, S. Fang, Robust exponential stability for uncertain stochastic neural networks with discrete distributed time-varying delays. Phys. Lett. A 372, 3385-3394 (2008)
7. H. Li, B. Chen, Q. Zhou, C. Lin, Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Phys. Lett. A 372, 4996-5003 (2008)
8. Y. Liu, Z. Wang, X. Liu, On global exponential stability of generalized stochastic neural networks with mixed time-delays. Neurocomputing 70, 314-326 (2006) (Pubitemid 44615800)
9. Y. Liu, Z. Wang, X. Liu, An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays. Nonlinear Anal.: Hybrid Syst. 2, 110-120 (2008)
10. X. Lou, B. T. Cui, Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J. Math. Anal. Appl. 328, 316-326 (2007)
11. X. Lou, B. T. Cui, Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. B 37, 713-719 (2007) (Pubitemid 46784604)
12. X. Mao, Robustness of exponential stability of stochastic differential delay equation. IEEE Trans. Automat. Contr. 41, 442-447 (1996) (Pubitemid 126767898)
13. X. Mao, Stochastic Differential Equations Their Applications (Horwood, Chichester, 1997)
14. M. Mariton, Jump Linear Systems in Automatic Control (Dekker, New York, 1990)
15. L. Wan, J. Sun, Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 343, 306-318 (2005)
16. Y. Wang, L. Xie, C. E. de Souza, Robust control of a class of uncertain nonlinear system. Syst. Control Lett. 19, 139-149 (1992) (Pubitemid 23572546)
17. Z. Wang, Y. Liu, K. Fraser, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete distributed delays. Phys. Lett. A 354, 288-297 (2006) (Pubitemid 43668651)
18. Z. Wang, Y. Liu, L. Yu, X. Liu, Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356, 346-352 (2006)
19. Z. Wang, H. Shu, J. Fang, X. Liu, Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal.: Real World Appl. 7, 1119-1128 (2006) (Pubitemid 43903684)
20. Z. Wang, J. Fang, X. Liu, Global stability of stochastic high-order neural networks with discrete distributed delays. Chaos Solitons Fractals 36, 388-396 (2008) (Pubitemid 47588902)
21. Y. Wang, Z. Wang, J. Liang, A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys. Lett. A 372, 6066-6073 (2008)
22. J. Yu, K. Zhang, S. Fei, Further results on mean square exponential stability of uncertain stochastic delayed neural networks. Commun. Nonlinear Sci. Numer. Simul. 14, 1582-1589 (2009)
23. D. Yue, Q.-L. Han, Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. IEEE Trans. Automat. Contr. 50, 217-222 (2005)
24. J. Zhang, P. Shi, J. Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays. Nonlinear Anal.: Real World Appl. 8, 1349-1357 (2007) (Pubitemid 46551830)