Delay-dependent stability criteria for reaction-diffusion neural networks with time-varying delays

IEEE Transactions on Cybernetics

Volumn 43, Issue 6, 2013, Pages 1913-1920

  Ma, Qian ^a   Feng, Gang ^a,b   Xu, Shengyuan ^a  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Asymptotic stability; Delay dependent stability criteria; Lyapunov Krasovskii functional; Reaction diffusion neural networks

Indexed keywords

DELAY DEPENDENT STABILITY CRITERION; GLOBAL ASYMPTOTIC STABILITY; LINEAR OPERATORS; LYAPUNOV-KRASOVSKII FUNCTIONALS; PARTIAL DIFFERENTIAL; REACTION-DIFFUSION NEURAL NETWORKS; SIMULATION EXAMPLE; TIME-VARYING DELAY;

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS; MATHEMATICAL OPERATORS; NEURAL NETWORKS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS;

DIFFUSION IN LIQUIDS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; THEORETICAL MODEL; TIME;

ALGORITHMS; COMPUTER SIMULATION; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 84890097051     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2012.2235178     Document Type: Article

References (38)

1. L. Chua and L. Yang, "Cellular neural networks: Applications," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273-1290, Oct. 1988.
2. J. Farrell and A. Michel, "A synthesis procedure for Hopfield's continuous-time associative memory," IEEE Trans. Circuits Syst., vol. 37, no. 7, pp. 877-884, Jul. 1990. (Pubitemid 20725112)
3. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci., vol. 81, no. 10, pp. 3088-3092, May 1984. (Pubitemid 14109528)
4. J. Cao and J. Wang, "Global asymptotic stability of a general class of recurrent neural networks with time-varying delays," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 1, pp. 34-44, Jan. 2003.
5. J. Cao and J. Wang, "Global asymptotic and robust stability of recurrent neural networks with time delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 2, pp. 417-426, Feb. 2005. (Pubitemid 40319475)
6. T. Li, W. Zheng, and C. Lin, "Delay-slope-dependent stability results of recurrent neural networks," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2138-2143, Dec. 2011.
7. Y. He, G. Liu, and D. Rees, "New delay-dependent stability criteria for neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 18, no. 1, pp. 310-314, Jan. 2007. (Pubitemid 46062938)
8. S. Mou, H. Gao, J. Lam, and W. Qiang, "A new criterion of delaydependent asymptotic stability for Hopfield neural networks with time delay," IEEE Trans. Neural Netw., vol. 19, no. 3, pp. 532-535, Mar. 2008. (Pubitemid 351411577)
9. J. H. Park, O. M. Kwon, and S. M. Lee, "LMI optimization approach on stability for delayed neural networks of neutral-type," Appl. Math. Comput., vol. 196, no. 1, pp. 236-244, Feb. 2008.
10. H. Shao and Q. Han, "New delay-dependent stability criteria for neural networks with two additive time-varying delay components," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 812-818, May 2011.
11. S. Xu and J. Lam, "A new approach to exponential stability analysis of neural networks with time-varying delays," Neural Netw., vol. 19, no. 1, pp. 76-83, Jan. 2006. (Pubitemid 43088737)
12. Z. Wang, Y. Liu, X. Liu, and Y. Shi, "Robust state estimation for discretetime stochastic neural networks with probabilistic measurement delays," Neurocomputing, vol. 74, no. 1-3, pp. 256-264, Dec. 2010.
13. X. Li, H. Gao, and X. Yu, "A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 41, no. 5, pp. 1275-1286, Oct. 2011.
14. H. R. Karimi and H. Gao, "New delay-dependent exponential H∞ synchronization for uncertain neural networks with mixed time-delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 1, pp. 173-185, Feb. 2010.
15. H. R. Karimi, "Robust delay-dependent H∞ control of uncertain Markovian jump systems with mixed neutral, discrete and distributed time-delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 8, pp. 1910-1923, Aug. 2011.
16. H. Li, B. Chen, Q. Zhou, and W. Qian, "Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 39, no. 1, pp. 94-102, Feb. 2009.
17. H. Zhang, Z. Liu, G. Huang, and Z.Wang, "Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 91-106, Jan. 2010.
18. Y. Liu, Z. Wang, J. Liang, and X. Liu, "Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays," IEEE Trans. Neural Netw., vol. 20, no. 7, pp. 1102-1116, Jul. 2009.
19. Q. Zhu and J. Cao, "Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 41, no. 2, pp. 341-353, Apr. 2011.
20. B. Zhang, S. Xu, G. Zong, and Y. Zou, "Delay-dependent exponential stability for uncertain stochastic Hopfield neural networks with timevarying delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 6, pp. 1241-1247, Jun. 2009.
21. S. Xu and J. Lam, "A survey of linear matrix inequality techniques in stability analysis of delay systems," Int J. Syst. Sci., vol. 39, no. 12, pp. 1095-1113, Dec. 2008.
22. J. Liang and J. Cao, "Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays," Phys. Lett. A, vol. 314, pp. 434-442, 2003.
23. L. Chua, M. Hasler, G. Moschytz, and J. Neirynck, "Autonomous cellular neural networks: A unified paradigm for pattern formation and active wave propagation," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 10, pp. 559-577, Oct. 1995.
24. P. Arena, L. Fortuna, and M. Frasca, "Multi-template approach to realize central pattern generators for artificial locomotion control," Int. J. Circuit Theory Appl., vol. 30, no. 4, pp. 441-458, Jul./Aug. 2002. (Pubitemid 34798633)
25. A. Adamatzky, P. Arena, A. Basile, R. Galan, B. Costello, L. Fortuna, M. Frasca, and A. Vazquez, "Reaction-diffusion navigation robot control: From chemical to VLSI analogic processors," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 5, pp. 926-938, May 2004.
26. L. Wang and Y. Cao, "Global exponential robust stability of reaction- diffusion interval neural networks with time-varying delays," Phys. Lett. A, vol. 350, no. 5/6, pp. 342-348, 2006. (Pubitemid 43129363)
27. Z. Zhang, Y. Yang, and Y. Huang, "Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays," Neural Netw., vol. 24, no. 5, pp. 457-465, Jun. 2011.
28. X. Li and J. Cao, "Delay-independent exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays and reaction- diffusion terms," Nonlinear Dyn., vol. 50, no. 1/2, pp. 363-371, Oct. 2007. (Pubitemid 47327552)
29. Z. Liu and J. Peng, "Delay-independent stability of stochastic reaction- diffusion neural networks with Dirichlet boundary conditions," Neural Comput. Appl., vol. 19, no. 1, pp. 151-158, Jan. 2010.
30. J. Lu, "Robust global exponential stability for interval reaction-diffusion Hopfield neural networks with distributed delays," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 12, pp. 1115-1119, Dec. 2007.
31. J. Lu, "Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos Solitons Fractals, vol. 35, no. 1, pp. 116-125, Jan. 2008. (Pubitemid 47385219)
32. J. Pan and S. Zhong, "Novel criteria on global robust exponential stability to a class of reaction-diffusion neural networks with Delays," Discrete Dyn. Nat. Soc., vol. 2009, pp. 291 594-1-291 594-14, 2009.
33. C. Hu, H. Jiang, and Z. Teng, "Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms," IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 67-81, Jan. 2010.
34. Z. S. Wang and H. Zhang, "Global asymptotic stability of reaction- diffusion Cohen-Grossberg neural networks with continuously distributed delays," IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 39-49, Jan. 2010.
35. Z. S.Wang, H. Zhang, and P. Li, "An LMI approach to stability analysis of reaction-diffusion Cohen-Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 40, no. 6, pp. 1596-1606, Dec. 2010.
36. L. C. Evans, Partial Differential Equations. Providence, RI: AMS, 1998.
37. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. 39th IEEE Conf. Decision Control, Sydney, Australia, 2000, pp. 2805-2810. (Pubitemid 32528463)
38. E. Fridman and Y. Orlov, "Exponential stability of linear distributed parameter systems with time-varying delays," Automatica, vol. 45, no. 1, pp. 194-201, Jan. 2009.