Improved delay-dependent stability condition of discrete recurrent neural networks with time-varying delays

IEEE Transactions on Neural Networks

Volumn 21, Issue 4, 2010, Pages 692-697

  Wu, Zhengguang ^a   Su, Hongye ^a   Chu, Jian ^a   Zhou, Wuneng ^b  

^a STATE KEY LABORATORY OF INDUSTRIAL CONTROL TECHNOLOGY   (China)

^b DONGHUA UNIVERSITY   (China)

Author keywords

Delay dependent; Exponential stability; Linear matrix inequality (LMI); Neural networks; Time varying delays

Indexed keywords

DELAY DEPENDENT EXPONENTIAL STABILITY; DELAY DEPENDENT STABILITY CRITERION; DELAY-DEPENDENT STABILITY CONDITION; EXPONENTIAL STABILITY; GLOBAL EXPONENTIAL STABILITY; LINEAR MATRIX INEQUALITY APPROACH; NUMERICAL EXAMPLE; TIME-VARYING DELAY;

EXPONENTIAL FUNCTIONS; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

RECURRENT NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; FEEDBACK SYSTEM; HUMAN; NONLINEAR SYSTEM; STATISTICAL MODEL; TIME;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; HUMANS; LINEAR MODELS; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; TIME FACTORS;

EID: 77950859442     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2010.2042172     Document Type: Article

References (21)

1. S. Arik, "Global asymptotic stability of a class of dynamical neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.47, no.2, pp. 568-571, Apr. 2000.
2. J. Cao, K. Yuan, and X. Li, "Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays," IEEE Trans. Neural Netw., vol.17, no.6, pp. 1646-1651, Nov. 2006. (Pubitemid 44824277)
3. W. Chen, X. Lu, and D. Liang, "Global exponential stability for discrete- time neural networks with variable delays," Phys. Lett. A, vol.358, no.3, pp. 186-198, 2006. (Pubitemid 44233178)
4. J. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
5. Y. He, M.Wu, G. Liu, and J. She, "Output feedback stabilization for a discrete-time system with a time-varying delay," IEEE Trans. Autom. Control, vol.35, no.11, pp. 2327-2377, Nov. 2008.
6. Y. He, Y. Zhang, M. Wu, and J. She, "Improved exponential stability for stochastic Markovian jump systems with nonlinearity and timevarying delay," Int. J. Robust Nonlinear Control, vol.20, no.1, pp. 16-26, 2010.
7. Y. Liu, Z.Wang, and X. Liu, "Asymptotic stability for neural networks with mixed time-delays: The discrete-time case," Neural Netw., vol.22, no.1, pp. 67-74, 2009.
8. Y. Liu, Z. Wang, A. Serrano, and X. Liu, "Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis," Phys. Lett. A, vol.362, no.5-6, pp. 480-488, 2007.
9. 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)
10. S. I. Niculescu and K. Gu, Eds., Advances in Time-Delay Systems. Berlin, Germany: Springer-Verlag, 2004.
11. C. Peng and Y. Tian, "Delay-dependent robust stability criteria for uncertain systems with interval time varying delay," J. Comput. Appl. Math., vol.214, no.2, pp. 480-494, 2008.
12. C. Song, H. Gao, and W. Zheng, "A new approach to stability analysis of discrete-time recurrent neural networks with time-varying delay," Neurocomputing, vol.72, no.10-12, pp. 2563-2568, 2009.
13. Q. Song and Z.Wang, "A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays," Phys. Lett. A, vol.368, no.1-2, pp. 134-145, 2007.
14. C. Sun and C. Bo, "Exponential periodicity of continuous-time and discrete-time neural networks with delays," Neural Process. Lett., vol.19, no.2, pp. 131-146, 2004.
15. Z. Wang, H. Shu, Y. Liu, D. W. C. Ho, and X. Liu, "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos Solitons Fractals, vol.30, no.4, pp. 886-896, 2006.
16. M. Wu, F. Liu, P. Shi, Y. He, and R. Yokoyama, "Improved freeweighting matrix approach for stability analysis of discrete-time recurrent neural networks with time-varying delay," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.55, no.7, pp. 690-694, Jul. 2008.
17. S. Xu and J. Lam, "On equivalence and efficiency of certain stability criteria for time-delay systems," IEEE Trans. Autom. Control, vol.52, no.1, pp. 95-101, Jan. 2007. (Pubitemid 46344002)
18. J. Yu, K. Zhang, and S. Fei, "Exponential stability criteria for discrete- time recurrent neural networks with time-varying delay," Nonlinear Anal.-Real World Appl., vol.11, no.1, pp. 207-216, 2010.
19. D. Yue, Y. Zhang, and E. Tian, "Improved global robust delay-dependent stability criteria for delayed cellular neural networks," Int. J. Comput. Math., vol.85, no.8, pp. 1265-1277, 2008.
20. B. Zhang, S. Xu, and Y. Zou, "Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with timevarying delays," Neurocomputing, vol.72, no.1-3, pp. 321-330, 2008.
21. X. Zhu and G.Yang, "Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay," in Proc. Amer. Control Conf., Seattle, WA, Jun. 2008, pp. 1644-1649.