Global exponential stability of impulsive neural networks with variable delay: An LMI approach

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 56, Issue 6, 2009, Pages 1248-1259

  Chen, Wu Hua ^a,b   Zheng, Wei Xing ^a  

^a UNIVERSITY OF WESTERN SYDNEY   (Australia)

^b GUANGXI UNIVERSITY   (China)

Author keywords

Exponential stability; Impulses; Linear matrix inequality (LMI); Neural networks; Variable delay

Indexed keywords

ASYMPTOTIC STABILITY; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; ROBUSTNESS (CONTROL SYSTEMS);

GLOBAL EXPONENTIAL STABILITY; IMPULSES; IMPULSIVE NEURAL NETWORKS; INPUT DISTURBANCE; RAZUMIKHIN-TYPE; STABILITY CONDITION; TIME SEQUENCES; VARIABLE DELAYS;

NEURAL NETWORKS;

EID: 67650377042     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.2006210     Document Type: Article

References (33)

1. C. M. Marcus and R. M. Westervelt, "Stability of analog neural networks with delay," Phys. Rev. A, vol. 39, pp. 347-359, 1989.
2. J. Cao, "Periodic oscillation and exponential stability of delayed CNNs," Phys. Lett. A, vol. 270, pp. 157-163, 2000.
3. K. Gopalsamy and X. Z. He, "Delay independent stability in bidirectional associative memory neural networks," IEEE Trans. Neural Netw., vol. 5, pp. 998-1002, 1994.
4. H. Ye and A. N. Michel, "Robust stability of nonlinear time-delay systems with applications to neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, pp. 532-543, 1996.
5. H.-D. Qi and L. Qi, "Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 99-109, 2004.
6. W.-H. Chen, Z.-H. Guan, and X. Lu, "Delay-dependent exponential stability of neural networks with variable delays," Phys. Lett. A vol. 326, pp. 355-363, 2004.
7. W.-H. Chen and X. Lu, "New delay-dependent exponential stability criteria for neural networks with variable delays," Phys. Lett. A vol. 351, pp. 53-58, 2006.
8. W.-H. Chen, X. Lu, and D.-Y. Liang, "Global exponential stability for discrete-time neural networks with variable delays," Phys. Lett. A vol. 358, pp. 186-198, 2006.
9. W.-H. Chen, X. Lu, Z.-H. Guan, and W. X. Zheng, "Delay-dependent exponential stability of neural networks with variable delay: An LMI approach," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 9, pp. 837-842, 2006.
10. W.-H. Chen and W. X. Zheng, "Global asymptotic stability of a class of neural networks with distributed delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 3, pp. 644-652, 2006.
11. W.-H. Chen and W. X. Zheng, "On global asymptotic stability of cohen-grossberg neural networks with variable delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 10, Oct. 2008.
12. Y. He, G. P. Liu, and D. Rees, "New delay-dependent stability criteria for neutral networks with time-varying delay," IEEE Trans. Neural Netw., vol. 18, pp. 310-314, 2007.
13. Y. He, M. Wu, and J.-H. She, "Delay-dependent exponential stability of delayed neural networks with time-varying delay," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 7, pp. 553-557, Jul. 2006.
14. D. D. Bainov and P. S. Simeonov, Systems With Impulse Effect: Stability, Theory and Applications. Chichester, U.K.: Ellis Horwood, 1989.
15. M. V. Basin and M. A. Pinsky, "Stability impulse control of faulted nonlinear systems," IEEE Trans. Autom. Control, vol. 43, no. 11, pp. 1604-1608, 1998.
16. H. Zhang, M. V. Basin, and M. Skliar, "Ito-Volterra optimal state estimation with continuous, multirate, randomly sampled, and delayed measurements," IEEE Trans. Autom. Control, vol. 52, no. 3, pp. 401-416, Mar. 2007.
17. Z.-H. Guan and G. Chen, "On delayed impulsive hopfield neural networks," Neural Netw., vol. 12, pp. 273-280, 1999.
18. Z.-H. Guan, J. Lam, and G. Chen, "On impulsive auto-associative neural networks," Neural Netw., vol. 13, pp. 63-69, 2000.
19. K. Gopalsamy, "Stability of artificial neural networks with impulses," Appl. Math. Comput., vol. 154, pp. 783-813, 2004.
20. Y. Li, "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, vol. 24, pp. 279-285, 2005.
21. Y. Xia, J. Cao, and S. S. Cheng, "Global exponential stability of delayed cellular neural networks with impulses," Neurocomputing, vol. 70, pp. 2495-2501, 2007.
22. Y. Yang and J. Cao, "Stability and periodicity in delayed cellular neural networks with impulsive effects," Nonlinear Analysis: Real World Applications, vol. 8, pp. 362-374, 2007.
23. Z. Chen and J. Ruan, "Global stability analysis of impulsive cohen-grossberg neural networks with delay," Phys. Lett. A, vol. 345, pp. 101-111, 2005.
24. D. W. C. Ho, J. Liang, and J. Lam, "Global exponential stability of impulsive high-order BAM neural networks with time-varying delays," Neural Netw., vol. 19, pp. 1581-1590, 2006.
25. Z. Yang and D. Xu, "Impulsive effects on stability of cohen-grossberg neural networks with variable delays," Appl. Math. Comput., vol. 177, pp. 63-78, 2006.
26. D. Xu and Z. Yang, "Impulsive delay differential inequality and stability of neural networks," J. Math. Anal. Appl., vol. 305, pp. 107-120, 2005.
27. Z. Yang and D. Xu, "Stability analysis of delay neural networks with impulsive effects," IEEE Trans. Circuits Syst. II, Anal. Digit. Signal Process., vol. 52, no. 8, pp. 517-521, Aug. 2005.
28. S. Long and D. Xu, "Delay-dependent stability analysis for impulsive neural networks with time varying delays," Neurocomput., vol. 71, pp. 1705-1713, 2008.
29. Y. Zhang and J. Sun, "Stability of impulsive neural networks with time delays," Phys. Lett. A, vol. 348, pp. 44-50, 2005.
30. X. Liu and G. Ballinger, "Uniform asymptotic stability of impulsive delay differential equations," Comput. Math. Appl., vol. 41, pp. 903-915, 2001.
31. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadephia, PA: SIAM, 1994.
32. Y. Wang, L. Xie, and C. E. de Souza, "Robust control of a class of uncertain nonlinear systems," Syst. Contr. Lett., vol. 19, pp. 139-149, 1992.
33. H. T. Lu, "Chaotic attractors in delayed neural networks," Phys. Lett. A, vol. 298, no. 2-3, pp. 109-116, 2002.