Lagrange stability of memristive neural networks with discrete and distributed delays

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 4, 2014, Pages 690-703

  Wu, Ailong ^a,b,c   Zeng, Zhigang ^c,d  

^a HUBEI NORMAL UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^d BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

Hybrid systems; Lagrange stability; Memristive neural networks; Nonsmooth analysis

Indexed keywords

HYBRID SYSTEMS; STABILITY CRITERIA;

ARTIFICIAL BRAIN; DISCRETE AND DISTRIBUTED DELAYS; GENERAL CLASS; LAGRANGE STABILITY; NETWORK PARAMETERS; NEUROMORPHIC SYSTEMS; NON-SMOOTH ANALYSIS;

NEURAL NETWORKS;

ALGORITHM; ANIMAL; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; BIOMIMETICS; COMPUTER SIMULATION; FEEDBACK SYSTEM; HUMAN; PROCEDURES; SIGNAL PROCESSING; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; BIOMIMETICS; COMPUTER SIMULATION; FEEDBACK; HUMANS; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84897021697     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2280458     Document Type: Article

References (46)

1. K. D. Cantley, A. Subramaniam, H. J. Stiegler, R. A. Chapman, and E. M. Vogel, "Hebbian learning in spiking neural networks with nanocrystalline silicon TFTs and memristive synapses," IEEE Trans. Nanotechnol., vol. 10, no. 5, pp. 1066-1073, Sep. 2011
2. K. D. Cantley, A. Subramaniam, H. J. Stiegler, R. A. Chapman, and E. M. Vogel, "Neural learning circuits utilizing nanocrystalline silicon transistors and memristors," IEEE Trans Neural Netw. Learn. Syst., vol. 23, no. 4, pp. 565-573, Apr. 2012
3. M. Itoh and L. O. Chua, "Memristor cellular automata and memristor discrete-time cellular neural networks," Int. J. Bifurcat. Chaos, vol. 19, no. 11, pp. 3605-3656, Nov. 2009
4. H. Kim, M. P. Sah, C. J. Yang, T. Roska, and L. O. Chua, "Neural synaptic weighting with a pulse-based memristor circuit," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 1, pp. 148-158, Jan. 2012
5. Y. V. Pershin and M. Di Ventra, "Experimental demonstration of associative memory with memristive neural networks," Neural Netw., vol. 23, no. 7, pp. 881-886, Sep. 2010
6. F. Z. Wang, N. Helian, S. N. Wu, X. Yang, Y. K. Guo, G. Lim, and M. M. Rashid, "Delayed switching applied to memristor neural networks," J. Appl. Phys., vol. 111, no. 7, pp. 07E317-1-07E317-3, 2012
7. A. L. Wu, S. P.Wen, and Z. G. Zeng, "Synchronization control of a class of memristor-based recurrent neural networks," Inf. Sci., vol. 183, no. 1, pp. 106-116, Jan. 2012
8. A. L. Wu and Z. G. Zeng, "Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays," Neural Netw., vol. 36, pp. 1-10, Dec. 2012
9. A. L. Wu and Z. G. Zeng, "Exponential stabilization of memristive neural networks with time delays," IEEE Trans. Neural Netw. Learn Syst., vol. 23, no. 12, pp. 1919-1929, Dec. 2012
10. H. Huang, G. Feng, and J. Cao, "Robust state estimation for uncertain neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 19, no. 8, pp. 1329-1339, Aug. 2008
11. T. W. Huang, "Robust stability of delayed fuzzy Cohen-Grossberg neural networks," Comput. Math. Appl., vol. 61, no. 8, pp. 2247-2250, Apr. 2011
12. T. W. Huang, C. D. Li, S. K. Duan, and J. A. Starzyk, "Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 6, pp. 866-875, Jun. 2012
13. X. Liu and J. Cao, "Robust state estimation for neural networks with discontinuous activations," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 40, no. 6, pp. 1425-1437, Dec. 2010
14. D. Liu, Z. Pang, and S. R. Lloyd, "A neural network method for detection of obstructive sleep apnea and narcolepsy based on pupil size and EEG," IEEE Trans. Neural Netw., vol. 19, no. 2, pp. 308-318, Feb. 2008 (Pubitemid 351359295)
15. Y. Liu, Z. Wang, and X. Liu, "State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays," Phys Lett. A, vol. 372, no. 48, pp. 7147-7155, Dec. 2008
16. Y. Shen and J. Wang, "Almost sure exponential stability of recurrent neural networks with Markovian switching," IEEE Trans. Neural Netw., vol. 20, no. 5, pp. 840-855, May 2009
17. Y. Shen and J.Wang, "Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 1, pp. 87-96, Jan. 2012
18. D. Wang, D. Liu, and Q. Wei, "Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach," Neurocomputing, vol. 78, no. 1, pp. 14-22, Feb. 2012
19. Z. Wang and D. Liu, "Data-based controllability and observability analysis of linear discrete-time systems," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2388-2392, Dec. 2011
20. Z. Wang, Y. Liu, and X. Liu, "State estimation for jumping recurrent neural networks with discrete and distributed delays," Neural Netw., vol. 22, no. 1, pp. 41-48, Jan. 2009
21. W. Wu and T. P. Chen, "Global synchronization criteria of linearly coupled neural network systems with time-varying coupling," IEEE Trans. Neural Netw., vol. 19, no. 2, pp. 319-332, Feb. 2008 (Pubitemid 351359296)
22. W. Wu, W. J. Zhou, and T. P. Chen, "Cluster synchronization of linearly coupled complex networks under pinning control," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 4, pp. 829-839, Apr. 2009
23. X. Yang, J. Cao, and J. Lu, "Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 1, pp. 60-71, Jan. 2012
24. X. Yang, J. Cao, and J. Lu, "Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 2, pp. 371-384, Feb. 2012
25. X. Yang, J. Cao, and J. Lu, "Synchronization of randomly coupled neural networks with Markovian jumping and time-delay," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 60, no. 2, pp. 363-376, Feb. 2013
26. Z. Yi, "Foundations of implementing the competitive layer model by Lotka-Volterra recurrent neural networks," IEEE Trans. Neural Netw., vol. 21, no. 3, pp. 494-507, Mar. 2010
27. Z. Yi, L. Zhang, J. L. Yu, and K. K. Tan, "Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks," IEEE Trans. Neural Netw., vol. 20, no. 6, pp. 952-963, Jun. 2009
28. W. Yu, P. C. Francisco, and X. Li, "Two-stage neural sliding mode control of magnetic levitation in minimal invasive surgery," Neural Comput. Appl., vol. 20, no. 8, pp. 1141-1147, Nov. 2011
29. W. Yu and X. Li, "Automated nonlinear system modeling with multiple fuzzy neural networks and kernel smoothing," Int. J. Neural Syst., vol. 20, no. 5, pp. 429-435, Oct. 2010
30. H. Zhang, J. Liu, D. Ma, and Z. Wang, "Data-core-based fuzzy min-max neural network for pattern classification," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2339-2352, Dec. 2011
31. H. Zhang, Y. Luo, and D. Liu, "Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints," IEEE Trans. Neural Netw., vol. 20, no. 9, pp. 1490-1503, Sep. 2009
32. H. Zhang, T. Ma, G. Huang, and Z. Wang, "Robust global exponential synchronization of uncertain chaotic delayed neural networks via dualstage impulsive control," IEEE Trans. Syst. Man Cybern., B, Cybern., vol. 40, no. 3, pp. 831-844, Jun. 2010
33. H. Zhang and Y. Wang, "Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays," IEEE Trans. Neural Netw., vol. 19, no. 2, pp. 366-370, Feb. 2008 (Pubitemid 351359302)
34. Q. Zhu and J. Cao, "Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 3, pp. 467-479, Mar. 2012
35. X. X. Liao, Q. Luo, and Z. G. Zeng, "Positive invariant and global exponential attractive sets of neural networks with timevarying delays," Neurocomputing, vol. 71, nos. 4-6, pp. 513-518, Jan. 2008 (Pubitemid 351168440)
36. X. X. Liao, Q. Luo, Z. G. Zeng, and Y. X. Guo, "Global exponential stability in Lagrange sense for recurrent neural networks with time delays," Nonlinear Anal. Real World Appl., vol. 9, no. 4, pp. 1535-1557, Sep. 2008 (Pubitemid 351685795)
37. Q. Luo, Z. G. Zeng, and X. X. Liao, "Global exponential stability in Lagrange sense for neutral type recurrent neural networks," Neurocomputing, vol. 74, no. 4, pp. 638-645, Jan. 2011
38. Z. W. Tu, J. G. Jian, and K. Wang, "Global exponential stability in Lagrange sense for recurrent neural networks with both timevarying delays and general activation functions via LMI approach," Nonlinear Anal. Real World Appl., vol. 12, no. 4, pp. 2174-2182, Aug. 2011
39. B. X. Wang, J. G. Jian, and M. H. Jiang, "Stability in Lagrange sense for Cohen-Grossberg neural networks with time-varying delays and finite distributed delays," Nonlinear Anal. Hybrid Syst., vol. 4, no. 1, pp. 65-78, Feb. 2010
40. X. H. Wang, M. H. Jiang, and S. L. Fang, "Stability analysis in Lagrange sense for a non-autonomous Cohen-Grossberg neural network with mixed delays," Nonlinear Anal. Theory Methods Appl., vol. 70, no. 12, pp. 4294-4306, Jun. 2009
41. S. P. Wen, Z. G. Zeng, and T. W. Huang, "Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays," Neurocomputing, vol. 97, pp. 233-240, Nov. 2012
42. G. D. Zhang, Y. Shen, and J. W. Sun, "Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays," Neurocomputing, vol. 97, pp. 149-154, Nov. 2012
43. G. D. Zhang, Y. Shen, Q. Yin, and J. W. Sun, "Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays," Inf. Sci., vol. 232, pp. 386-396, May 2013
44. X. X. Liao, Theory and Applications of Stability for Dynamical Systems Beijing, China: National Defence Industry Press, 2000
45. K. Q. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. 39th Proc. IEEE Conf. Decision Control, Sydney, Australia, Dec. 2000, pp. 2805-2810
46. Z. G. Zeng and W. X. Zheng, "Multistability of neural networks with time-varying delays and concave-convex characteristics," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 293-305, Feb. 2012