Exponential Stability of Discrete-Time Delayed Hopfield Neural Networks with Stochastic Perturbations and Impulses
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- 作者：Shukai Duan (1) duansk@swu.edu.cn
Wenfeng Hu (2) hwfchongqing@yahoo.com.cn
Chuandong Li (2) licd@cqu.edu.cn
Sichao Wu (2) wscfrank@sina.com - 关键词：Mean square exponential stability – ; discrete ; time Hopfiled neural networks – ; stochastic perturbations – ; impulse – ; Lyapunov– ; Krasovskii function – ; Halanay inequality
- 刊名：Results in Mathematics
- 出版年：2012
- 出版时间：September 2012
- 年：2012
- 卷：62
- 期：1-2
- 页码：73-87
- 全文大小：301.9 KB
- 参考文献：1. Hopfield J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. USA 79, 2554–2558 (1982)
2. Hopfield J.J.: Neurons with graded response have collective computational like those of two-state neurons. Proc. Nat. Acad. Sci. USA 1, 3088–3092 (1984)
3. Guan Z.H., Chen G.R., Qin Y.: On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans. Neural Netw. 11(2), 534–540 (2000)
4. Gopalsamy K., He X.Z.: Stability in asymmetric Hopfield nets with transmission delays. Phys. D 76(4), 344–358 (1984)
5. Arik S.: Stability analysis of delayed neural networks. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(7), 1089–1092 (2000)
6. Cao J.D., Yuan K., Li H.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17(6), 1646–1651 (2007)
7. Cao J.D., Wang L.: Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Netw. 13, 457–463 (2002)
8. Liu X.Z., Teo K.L.: Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. IEEE Trans. Neural Netw. 16, 1329–1339 (2005)
9. Liao X.F., Chen G.R., Sanchez E.N.: Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Netw. 15, 855–866 (2002)
10. Song Q., Wang Z.D.: A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays. Phys. Lett. A 368, 134–145 (2007)
11. Li, C.D., Liao, X.F., Zhang, R.: A global exponential robust stability criterion for interval delayed neural networks with variable delays. 69(7–9), 803–809 (2006)
12. Li C.D., Shen Y.Y., Feng G.: Stabilizing effects of impulse in delayed BAM neural networks. IEEE Trans. Circuits Syst. II 53(12), 1284–1288 (2008)
13. Li C.D., Feng G., Huang T.W.: On hybrid impulsive and switching neural networks. IEEE Trans. Syst. Man Cybern. B 38(6), 1549–1560 (2008)
14. Song Q.K., Cao J.D.: Impulsive effects on stability of fuzzy Cohen–Grossberg neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 37, 733–741 (2007)
15. Xu D., Yang Z.: Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, 107–120 (2005)
16. Liu X.Z.: stability results for impulsive differential system with applications to populations growth models. Dynam. Stabil. Syst. 9(2), 163–174 (1994)
17. Liu X.Z., Shen X.M., Zhang Y., Wang Q.: stability criteria for impulsive systems with time delay and unstable system matrices. IEEE Trans. Circuits Syst. 54(10), 2288–2298 (2007)
18. Zhang H., Chen L.S.: Asymptotic behavior of discrete solutions to delayed neural networks with impulses. Neurocomputing 71, 1032–1038 (2008)
19. Guan Z.H., Chen G.R.: On delayed impulsive Hopfield neural networks. Neural Netw. 12, 273–280 (1999)
20. Yang T.: Impulsive Control Theory. Springer, Berlin (2001)
21. Mohamad S., Gopalsamy K.: Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math. Comput. Simul. 53, 17–38 (2000)
22. Liz E., Ferreiro J.B.: A note on the global stability of generalized difference equations. Appl. Math. Lett. 15, 655–659 (2002)
23. Sun Y.H., Cao J.D., Wang Z.D.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70, 2477–2485 (2007)
24. Huang C.X., Cao J.D.: On pth moment exponential stability of stochastic Cohen–Grossbergneural networks with time-varying delays. Neurocomputing 73, 986–990 (2010)
25. Li X.D.: Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects. Neurocomputing 73, 749–758 (2010)
26. Ou Y., Liu H.Y., Si Y.L., Feng Z.G.: Stability analysis of discrete-time stochastic neural networks with time-varying delays. Neurocomputing 73, 740–748 (2010)
27. Liu B.: Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Trans. Autom. Control 53(9), 2128–2133 (2008)
28. Li B., Xu D.: Mean square asymptotic behavior of stochastic neural networks with infinitely distributed delays. Neurocomputing 72, 3311–3317 (2009)
29. Liu Y.R., Wang Z.D., Liu X.H.: Robust stability of discrete-time stochastic neural networks with time-varying delays. Neurocomputing 71, 823–833 (2008)
30. Desmond J., Higham D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. Siam Rev. 43(3), 525–546 (2001)
31. Boyed S., Ghaoui L., Feron E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) - 作者单位：1. School of Electronics and Information Engineering, Southwest University, Chongqing, 400715 China2. College of Computer, Chongqing University, Chongqing, 400044 China
- ISSN：1420-9012
文摘
This paper derives some sufficient conditions for exponential stability in the mean square of stochastic discrete-time delayed Hopfield neural networks (DHNN) with impulse effects. The Lyapunov–Krasovskii stability theory, Halanay inequality, and linear matrix inequality (LMI) are employed to investigate the problem. It is shown that the impulses in certain regions might preserve the stability property of the DHNN when the impulses-free part converges to its equilibrium point. Moreover, the feasible interval of the jump operator is also derived.