Global exponential stability for a class of generalized delayed neural networks with impulses

Mathematical Methods in the Applied Sciences

Volumn 34, Issue 11, 2011, Pages 1414-1420

  Xi, Qiang ^a  

^a SHANDONG UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

delays; equilibrium; generalized neural networks; global exponential stability; impulses

Indexed keywords

DELAYED NEURAL NETWORKS; DELAYS; EQUILIBRIUM POINT; GENERALIZED NEURAL NETWORK; GLOBAL EXPONENTIAL STABILITY; IMPULSES; LINEAR MATRIX INEQUALITY APPROACH; LYAPUNOV FUNCTIONAL METHOD; NEGATIVE DEFINITE MATRIX;

EXPONENTIAL FUNCTIONS; LINEAR MATRIX INEQUALITIES; STABILITY; TIME VARYING NETWORKS;

NEURAL NETWORKS;

EID: 79959695635     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1451     Document Type: Article

References (29)

1. Avitabile G, Forti M, Manetti S, Marini M, On a class of nonsymmetrical neural networks with application to ADC. IEEE Transactions on Circuits and Systems 1991; 38: 202-209.
2. Wang R, Tang Z, Cao Q, A learning method in Hopfield neural network for combinatorial optimization problem. Neurocomputing 2002; 48: 1021-1024. (Pubitemid 36221541)
3. Liu D, Michel A, Asymptotic stability of discrete time systems with saturation nonlinearities with applications to digital filters. IEEE Transactions on Circuits and Systems 1992; 39: 798-807. (Pubitemid 23629800)
4. Chen Z, Ruan J, Global stability analysis of impulsive Cohen-Grossberg neural networks with delay. Physics Letters A 2005; 345: 101-111. (Pubitemid 41277049)
5. Liao X, Li C, Wong K, Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 2004; 17: 1401-1414. (Pubitemid 39487137)
6. Li X, Global exponential stability for a class of neural networks. Applied Mathematics Letters 2009; 22: 1235-1239.
7. Balasubramaniam P, Rakkiyappan R, Global exponential stability for neutral-type BAM neural networks with time-varying delays. International Journal of Computer Mathematics 2010; 87: 2064-2075.
8. Zhang Q, Wei X, Xu J, Delay-dependent global stability results for delayed Hopfield neural networks. Chaos, Solitons and Fractals 2007; 34: 662-668. (Pubitemid 46561307)
9. Zhang Q, Wei X, Xu J, Delay-dependent global stability condition for delayed Hopfield neural networks. Nonlinear Analysis, Theory, Methods, Applications 2007; 8: 997-1002. (Pubitemid 46097521)
10. Hou Y, Liao T, Yan J, Global asymptotic stability for a class of nonlinear neural networks with multiple delays. Nonlinear Analysis, Theory, Methods, Applications 2007; 67: 3037-3040. (Pubitemid 47187932)
11. Xu S, Lam J, A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Networks 2006; 19: 76-83. (Pubitemid 43088737)
12. Li X, Bohner M, Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback. Mathematical and Computer Modelling 2010; 52: 643-653.
13. Li X, Global exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 2009; 73: 525-530.
14. Lou X, Cui B, Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. Journal of Mathematical Analysis and Applications 2007; 330: 144-158.
15. Li Y, Xing W, Lu L, Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons and Fractals 2006; 27: 437-445. (Pubitemid 41037127)
16. Yue D, Zhang Y, Tian E, Improved global robust delay-dependent stability criteria for delayed cellular neural networks. International Journal of Computer Mathematics 2008; 85: 1265-1277.
17. Berman A, Plemmons RJ, Nonnegative Matrices in Mathematical Sciences. Academic Press: New York, 1979.
18. Li X, Chen Z, Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Analysis, Theory, Methods, Applications 2009; 10: 3253-3265.
19. Xia Y, Cao J, Han M, A new analytical method for the linearization of dynamic equation on measure chains. Journal of Differential Equations 2007; 235: 527-543.
20. Xia Y, Han M, New conditions on the existence and stability of periodic solution in Lotka-Volterra's population system. SIAM Journal on Applied Mathematics 2009; 69: 1580-1597.
21. Xia Y, Yang Z, Han M, Lag synchronization of chaotic delayed Yang-Yang type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification. IEEE Transactions on Neural Networks 2009; 20: 1165-1180.
22. Zhou L, Li C, Wan J, Global Stability of discrete-time recurrent neural networks with impulse effects. International Symposium on Nonlinear Dynamics, Shanghai, China, vol. 10, 2008; 93-97.
23. Huang Z, Luo X, Yang Q, Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse. Chaos, Solitons and Fractals 2007; 34: 878-885. (Pubitemid 46601902)
24. Chen Z, Ruan J, Global dynamic analysis of general Cohen-Grossberg neural networks with impulse. Chaos, Solitons and Fractals 2007; 32: 1830-1837. (Pubitemid 46136971)
25. Bainov D, Simennov P, Systems with Impulsive Effect Stability Theory and Applications. Ellis Horwood Limited: New York, 1989.
26. Fu X, Yan B, Liu YS, Introduction of Impulsive Differential Systems. Science Press: Beijing, 2005.
27. Liu X, Wang Q, The method of Lyapunov functionals and exponential stability of impulsive systems with time delay. Nonlinear Analysis, Theory, Methods, Applications 2007; 66: 1465-1484. (Pubitemid 46072680)
28. Li X, Uniform asymptotic stability and global stability of impulsive infinite delay differential equations. Nonlinear Analysis, Theory, Methods, Applications 2009; 70: 1975-1983.
29. Li X, New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays. Nonlinear Analysis: Real World Applications 2010; 11: 4194-4201.