Stability of stochastic Markovian jump neural networks with mode-dependent delays

Neurocomputing

Volumn 74, Issue 12-13, 2011, Pages 2157-2163

  Ma, Qian ^a   Xu, Shengyuan ^a   Zou, Yun ^a   Lu, Jinjun ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NANTONG UNIVERSITY   (China)

Author keywords

Asymptotic stability; Markovian jumping parameters; Mixed mode dependent delays; Stochastic neural networks

Indexed keywords

DELAY DEPENDENT CONDITIONS; GENERAL CLASS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMPING PARAMETERS; MARKOVIAN JUMPS; MARKOVIAN SWITCHING; MEAN SQUARE; MIXED MODE-DEPENDENT DELAYS; NUMERICAL EXAMPLE; STABILITY ANALYSIS; STOCHASTIC NEURAL NETWORK;

ASYMPTOTIC STABILITY; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STOCHASTIC SYSTEMS; SWITCHING SYSTEMS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

NEURAL NETWORKS;

ANALYTIC METHOD; ANALYTICAL PARAMETERS; ARTICLE; ARTIFICIAL NEURAL NETWORK; LINEAR SYSTEM; LYAPUNOV KRASOVSKII FUNCTIONAL; MARKOVIAN JUMP; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; PRIORITY JOURNAL; STATISTICS;

EID: 79956113019     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2011.01.016     Document Type: Article

References (35)

1. Arik S. Global asymptotic stability of a large class of delayed cellular neural networks with constant delay. Phys. Lett. A 2002, 311:504-511.
2. Cao J., Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 2005, 52:417-426.
3. Cao J. Global stability conditions for delayed CNNs. IEEE Trans. Circuits Syst. I 2001, 48:1330-1333.
4. Farrell J., Michel A. A synthesis procedure for Hopfield's continuous-time associative memory. IEEE Trans. Circuits Syst. I 1990, 37:877-884.
5. K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 2805-2810.
6. He Y., Liu G., Rees D. New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Networks 2007, 18:310-314.
7. Ji Y., Chizeck H.J. Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Autom. Control 1990, 35:777-788.
8. Li T., Guo L., Lin C. Stability criteria with less LMI variables for neural networks with time-varying delay. IEEE Trans. Circuits Syst. II 2008, 55:1188-1192.
9. Liu Y., Wang Z., Liang J., Liu X. An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays. Nonlinear Anal. Hybrid Syst. 2008, 2:110-120.
10. Li H., Chen B., Zhou Q., Lin C. Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Phys. Lett. A 2008, 372:4996-5003.
11. Lou X., Cui B. Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J. Math. Anal. Appl. 2007, 328:316-326.
12. Ou Y., Shi P., Liu H. A mode-dependent stability criterion for delayed discrete-time stochastic neural networks with Markovian jumping parameters. Neurocomputing 2010, 73:1491-1500.
13. Shen H., Xu S., Song X., Chu Y. Delay-dependent H∞ filtering for stochastic systems with Markovian switching and mixed mode-dependent delays. Nonlinear Anal. Hybrid Syst. 2010, 4:122-133.
14. Sanchez E.N., Perez J.P. Input-to-state stability analysis for dynamic neural networks. IEEE Trans. Circuits Syst. I 1999, 46:1395-1398.
15. Wang Z., Liu Y., Yu L., Liu X. Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 2006, 356:346-352.
16. Xu S., Lam J., Ho D.W.C. A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks. IEEE Trans. Circuits Syst. II 2006, 53:230-234.
17. Xu S., Chen T., Lam J. Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Autom. Control 2003, 48:900-908.
18. Xu S., Lam J., Mao X. Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I 2007, 54:2070-2078.
19. Xu S., Zheng W., Zou Y. Passivity analysis of neural networks with time-varying delays. IEEE Trans. Circuits Syst. II 2009, 56:325-329.
20. Yue D., Zhang Y., Tian E. Improved global robust delay-dependent stability criteria for delayed cellular neural networks. Int. J. Comput. Math. 2008, 85:1265-1277.
21. Zhang B., Xu S. Robust H∞ filtering for uncertain discrete piecewise time-delay systems. Int. J. Control 2007, 80:636-645.
22. Zhang B., Xu S., Zou Y. Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays. Neurocomputing 2008, 72:321-330.
23. Zhang B., Xu S., Zou Y. Output feedback stabilization for delayed large-scale stochastic systems with Markovian jumping parameters. Asian J. Control 2009, 11:457-460.
24. Zhou Q., Chen B., Lin C., Li H. Mean square exponential stability for uncertain delayed stochastic neural networks with Markovian jump parameters. Circuits Syst. Signal Process. 2010, 29:331-348.
25. Zhang H., Wang Y. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Networks 2008, 19:366-370.
26. Zhang Y., Xu S., Zhang B. Robust output feedback stabilization for uncertain discrete-time fuzzy Markovian jump systems with time-varying delays. IEEE Trans. Fuzzy Syst. 2009, 17:411-420.
27. Zhou W., Lu H., Duan C. Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity. Neurocomputing 2009, 72:3357-3365.
28. Zhu Q., Cao J. Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Networks 2010, 21:1314-1325.
29. Zhu Q., Cao J. Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans. Syst. Man Cybern. B 2011, 41:341-353.
30. Zhu Q., Cao J. Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing 2010, 73:2671-2680.
31. Zhu Q., Yang X., Wang H. Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. J. Franklin Inst. 2010, 347:1489-1510.
32. Zhu Q., Cao J. Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays. Discrete Dyn. Nat. Soc. 2009, 20.
33. Mao X. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 2002, 47:1604-1612.
34. Zhao H., Xu S., Zou Y. Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent distributed delays. Int. J. Adapt. Control Signal Process. 2010, 24:83-94.
35. R.Z. Khasminskii, Stochastic Stability of Differential Equations, Alphen aan den Rijn, Sijthoffand Noor, Khasminskiidhoff, 1980.