Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

Nonlinear Dynamics

Volumn 57, Issue 1-2, 2009, Pages 209-218

  Wang, Guanjun ^a   Cao, Jinde ^a   Liang, Jinling ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Lyapunov functional; Markov process; Neural networks; Stability in the mean square; Time delays

Indexed keywords

CONTINUOUS TIME; DISTRIBUTED TIME; EXPONENTIAL STABILITY; EXPONENTIALLY STABLE; INEQUALITY TECHNIQUES; JUMPING PARAMETERS; LYAPUNOV FUNCTIONAL; LYAPUNOV FUNCTIONALS; MARKOVIAN JUMPING PARAMETERS; MEAN SQUARE; MIXED DELAYS; STABILITY ANALYSIS; STABILITY CONDITION; STABILITY IN THE MEAN SQUARE; STOCHASTIC ANALYSIS; STOCHASTIC NEURAL NETWORK;

MARKOV PROCESSES; STABILITY; TIME DELAY;

NEURAL NETWORKS;

EID: 67449151971     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9433-4     Document Type: Article

References (22)

1. J. Cao 1999 On stability of delayed cellular neural networks Phys. Lett. A 261 303 308
2. J. Cao J. Wang 2003 Global asymptotic stability of a general class of recurrent neural networks with time-varying delays IEEE Trans. Circ. Syst. I 50 34 44
3. J. Liang J. Cao 2003 Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays Phys. Lett. A 314 434 442
4. S. Arik 2004 An analysis of exponential stability of delayed neural networks with time varying delays Neural Netw. 17 1027 1031 (Pubitemid 39093820)
5. S. Xu J. Lam D.W.C. Ho 2005 Novel global asymptotical stability criteria for delayed cellular neural networks IEEE Trans. Circ. Syst. II 52 349 353 (Pubitemid 40986454)
6. J. Cao K. Yuan H.X. Li 2006 Global asymptotical stability of generalized recurrent neural networks with multiple discrete delays and distributed delays IEEE Trans. Neural Netw. 17 6 1646 1651 (Pubitemid 44824277)
7. Haykin, S.: Neural Networks. Prentice Hall, New York (1994)
8. X. Liao X. Mao 1996 Exponential stability and instability of stochastic neural networks Stoch. Anal. Appl. 14 165 185 (Pubitemid 126717957)
9. Mao, X.: Exponential Stability of Stochastic Differential Equations. Marcel Dekker, New York (1994)
10. S. Blythe X. Mao X. Liao 2001 Stability of stochastic delay neural networks J. Franklin Inst. 338 481 495 (Pubitemid 32446621)
11. L. Wan J. Sun 2005 Mean square exponential stability of stochastic delayed Hopfield neural networks Phys. Lett. A 343 306 318 (Pubitemid 40942026)
12. H. Zhao N. Ding 2006 Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays Appl. Math. Comput. 183 464 470 (Pubitemid 44908624)
13. Z. Wang S. Lauria J. Fang X. Liu 2007 Exponential stability of uncertain stochastic neural networks with mixed time-delays Chaos Solitons Fractals 32 62 72 (Pubitemid 44374960)
14. Y. Sun J. Cao 2007 Pth moment exponential stability of stochastic recurrent neural networks with time-varying delays Nonlinear Anal.: Real World Appl. 8 1171 1185 (Pubitemid 46551827)
15. D.D. Sworder R.O. Rogers 1983 An LQ-solution to a control problem associated with solar thermal central receiver IEEE Trans. Autom. AC-28 971 978 (Pubitemid 14484289)
16. Willsky, A.S., Rogers, B.C.: Stochastic stability research for complex power systems. DOE Contract, LIDS, Mass. Inst. Technol., Cambridge, MA, Rep. ET-76-C-01-2295 (1979)
17. X. Mao 2002 Exponential stability of stochastic delay interval systems with Markovian switching IEEE Trans. Autom. Control 47 1604 1612 (Pubitemid 35298547)
18. X. Lou B. Cui 2007 Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters J. Math. Anal. Appl. 328 316 326
19. Z. Wang Y. Liu L. Yu X. Liu 2006 Exponential stability of delayed recurrent neural networks with Markovian jumping parameters Phys. Lett. A 356 346 352 (Pubitemid 43947472)
20. H. Huang D.W.C. Ho Y. Qu 2007 Robust stability of stochastic delayed additive neural networks with Markovian switching Neural Netw. 20 799 809 (Pubitemid 47361677)
21. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
22. Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE Conference on Decision and Control, pp. 2805-2810. Sydney, Australia (2000) (Pubitemid 32528463)