NOVEL STABILITY CRITERIONS FOR TWO TYPES OF RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

Wenguang Luo, Yonghua Liu , Guangming Xie, and Hongli Lan

References

  1. [1] L.O. Chua and L. Yang, Cellular neural networks: applications,IEEE Transactions on Circuits and Systems, 35(10), 1988,1273–1290.
  2. [2] R.T. Bambang, K. Uchida, and R.R. Yacoub, Active noisecontrol in free space using recurrent neural networks withEKF algorithm, Control and Intelligent Systems, 36(3), 2008,201–1850.
  3. [3] J.A. Farrell and A.N. Michel, A synthesis procedure for Hop-field’s continuous-time associative memory, IEEE Transactionson Circuits and Systems, 37(7), 1990, 877–884.
  4. [4] A.N. Michel, J.A. Farrell, and F.H. Sun, Analysis and synthesistechniques for Hopfield type synchronous discrete-time neu-ral networks with applications to associative memory, IEEETransactions on Circuits and Systems, 37(11), 1990, 1356–1366.
  5. [5] Y.H. Chen and S.C. Fang, Neurocomputing with time delayanalysis for solving convex quadratic programming problems,IEEE Transactions on Neural Networks, 11(1), 2000, 230–240.
  6. [6] D.L. Wang, Emergent synchrony in locally coupled neuraloscillators, IEEE Transactions on Neural Networks, 6(4), 1995,941–948.
  7. [7] B.Y. Zhu, Q.L. Zhang, and S.C. Tong, The stability criterrionsfor fuzzy descriptor systems with time-delay, Control andIntelligent Systems, 35(3), 2007, 201–1750.
  8. [8] A. Birouche, B. Mourllion, and M. Basset, Model reduction fordiscrete-time switched linear time-delay systems via the H∞198robust stability, Control and Intelligent Systems, 39(1), 2011,201–2245.
  9. [9] M. Sedraoui, S. Gherbi, and S. Abdelmalek, A robust controllerbased on fractional structure for MIMO plant with multipledelays, Control and Intelligent Systems, 40(2), 2012, 201–2216.
  10. [10] T. Yang, L. Yang, C.W. Wu, and L.O. Chua, Fuzzy cellularneural networks: applications, Proc. of the IEEE Int. Workshopon Cellular Neural Networks and Applications, Seville, SP,1996, 181–186.
  11. [11] T. Yang and L. Yang, The global stability of fuzzy cellularneural network, IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, 43(10), 1996, 880–883.
  12. [12] S. Haykin, Neural networks: a comprehensive foundation (NewYork, NY: Macmillan College Publishing Company, 1994).
  13. [13] A. Friedman, Stochastic differential equations and applications(Berlin Heidelberg: Springer, 2011).
  14. [14] C. Lien and L. Chung, Global asymptotic stability for cellularneural networks with discrete and distributed time-varyingdelays, Chaos, Solitons and Fractals, 34(4), 2007, 1213–1219.
  15. [15] X. Liao, K. Wong, and C. Li, Global exponential stabilityfor a class of generalized neural networks with distributeddelays, Nonlinear Analysis: Real World Applications, 5(3),2004, 527–547.
  16. [16] K. Ma, L. Yu, and W. Zhang, Global exponential stabilityof cellular neural networks with time-varying discrete anddistributed delays, Neurocomputing, 72(10–12), 2009, 2705–2709.
  17. [17] Q. Song and Z. Wang, Neural networks with discrete anddistributed time-varying delays: a general stability analysis,Chaos, Solitons and Fractals, 37(5), 2008, 1538–1547.
  18. [18] J.H. Park and H.J. Cho, A delay-dependent asymptotic stabilitycriterion of cellular neural networks with time-varying discreteand distributed delays, Chaos, Solitons and Fractals, 33(2),2007, 436–442.
  19. [19] S. Fang, M. Jiang, and X. Wang, Exponential convergenceestimates for neural networks with discrete and distributeddelays, Nonlinear Analysis: Real World Applications, 10(2),2009, 702–714.
  20. [20] Y. Liu, Z. Wang, and X. Liu, Asymptotic stability for neu-ral networks with mixed time-delays: the discrete-time case,Neural Networks, 22(1), 2009, 67–74.
  21. [21] P. Balasubramaniam and M. Syed Ali, Stability analysis ofTakagi–Sugeno stochastic fuzzy Hopfield neural networks withdiscrete and distributed time varying delays, Neurocomputing,74(10), 2011, 1520–1526.
  22. [22] R. Rakkiyappan and P. Balasubramaniam, Delay-dependentasymptotic stability for stochastic delayed recurrent neuralnetworks with time varying delays, Applied Mathematics andComputation, 198(1), 2008, 526–533.
  23. [23] Y. Guo, Mean square global asymptotic stability of stochasticrecurrent neural networks with distributed delays, AppliedMathematics and Computation, 215(2), 2009, 791–795.
  24. [24] L. Chen and H. Zhao, Stability analysis of stochastic fuzzycellular neural networks with delays, Neurocomputing, 72(1–3),2008, 436–444.
  25. [25] S. Long and D. Xu, Stability analysis of stochastic fuzzy cellularneural networks with time-varying delays, Neurocomputing,74(14–15), 2011, 2385–2391.
  26. [26] L. Chen, R. Wu, and D. Pan, Mean square exponential stabilityof impulsive stochastic fuzzy cellular neural networks withdistributed delays, Expert Systems with Applications, 38(5),2011, 6294–6299.
  27. [27] M. Syed Ali and P. Balasubramaniam, Global asymptotic sta-bility of stochastic fuzzy cellular neural networks with multiplediscrete and distributed time-varying delays, Communicationsin Nonlinear Science and Numerical Simulation, 16(7), 2011,2907–2916.
  28. [28] H. Zhang, Z. Wang, and D. Liu, Robust exponential stability forrecurrent neural networks with multiple time-varying delays,IEEE Transactions on Circuits and Systems II: Express Briefs,54(8), 2007, 730–734.
  29. [29] Z. Liu, H. Zhang, and Z. Wang, Novel stability criterions of anew fuzzy cellular neural networks with time-varying delays,Neurocomputing, 72(4–6), 2009, 1056–1064.
  30. [30] J. Yu, K. Zhang, S. Fei, and T. Li, Simplified exponentialstability analysis for recurrent neural networks with discreteand distributed time-varying delays, Applied Mathematics andComputation, 205(1), 2008, 465–474.

Important Links:

Go Back