Novel Conditions for Robust Stability of Bidirectional Associative Memory Neural Networks with Multiple Time Delays

Yıl 2017, Cilt: 17 Sayı: 1, 3227 - 3238, 27.03.2017

Eylem Yucel

Öz

This paper deals with the problem of robust stability of the class of bidirectional associative memory (BAM) neural networks with multiple time delays. Several new sufficient conditions that imply the existence, uniqueness and global robust stability of the equilibrium point for the class of BAM neural networks are obatined by the use of the proper Lyapunov functionals and exploiting the norm properties of the interval matrices. The derived results basically depend on the system parameters of neural network model and they are independent of the time delays. We also give some numerical examples to show the applicability and novelty of the results, and compare the results with the corresponding robust stability results derived in the previous literature.

Anahtar Kelimeler

Robust Stability, BAM Neural Networks, Lyapunov Theorems, Interval Matrices

Kaynakça

• [1] C-D. Zheng, H. Zhang and Z. Wang, “Novel Exponential Stability Criteria of High-Order Neural Networks With Time-Varying Delays”, IEEE Transactions On Systems Man And Cybernetics Part B:Cybernetics , vol. 41, no. 2, pp. 486-496, 2011
• [2] Q. Song and Z. Wang, “Neural networks with discrete and distributed time-varying delays: A general stability analysis”, Chaos, Solitons and Fractals, vol. 37, no. 5, pp. 1538-1547, 2008.
• [3] Y. He, G.P. Liu, D. Rees and M. Wu, “Stability analysis for neural networks with time-varying interval delay”, IEEE Transactions On Neural Networks, vol. 18, no. 6, pp. 1850-1854, 2007.
• [4] X. Meng, M. Tian and S. Hu, “Stability analysis of stochastic recurrent neural networks with unbounded time-varying delays”, Neurocomputing, vol. 74, no. 6, pp. 949-953, 2011.
• [5] H. Zhang, Z. Wang, and D. Liu, “Global asymptotic stability of recurrent neural networks with multiple time varying delays”, IEEE Transactions on Neural Networks, vol. 19, no. 5, pp. 855873, 2008.
• [6] R. Yang, Z. Zhang and P. Shi, “Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays”, IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 169-175, 2010.
• [7] R.-S. Gau, C.-H. Lien and J.-G. Hsieh, “Novel Stability Conditions For Interval Delayed Neural Networks With Multiple Time-Varying Delays”, International Journal Of Innovative Computing Information And Control, vol. 7, no. 1, pp. 433-444, 2011.
• [8] Z. Liu, H. Zhang and Q. Zhang, “Novel Stability Analysis for Recurrent Neural Networks with Multiple Delays via Line Integral-Type L-K Functional”, IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1710-1718, 2010.
• [9] Z. Zuo, C. Yang and Y. Wang, “A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay”, IEEE Transactions on Neural Networks, vol. 21, no. 2, pp. 339-344, 2010.
• [10] Z.-G. Wu, Ju H. Park, H. Su and J. Chu, “New results on exponential passivity of neural networks with time-varying delays”, Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1593-1599, 2012.
• [11] D.H. Ji, J.H. Koo, S.C. Won, S.M. Lee and Ju H. Park, “Passivity-based control for Hopfield neural networks using convex representation”, Applied Mathematics and Computation, vol. 217, no. 13, pp. 6168-6175, 2011.
• [12] P. Balasubramaniam and S. Lakshmanan, “Delay-range dependent stability criteria for neural networks with Markovian jumping parameters”, Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 749-756, 2009.
• [13] H. Zhang, Z. Wang and D. Liu, “Global Asymptotic Stability and Robust Stability of a Class of Cohen-Grossberg Neural Networks With Mixed Delays”, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 56, no. 3, pp. 616-629, 2009.
• [14] P. Balasubramaniam and M.S. Ali, “Robust stability of uncertain fuzzy cellular neural networks with time-varying delays and reaction diffusion terms”, Neurocomputing, vol. 74, no. 1-3; pp. 439-446, 2010.
• [15] W.-H. Chen and W.X. Zheng, “Robust Stability Analysis for Stochastic Neural Networks With Time-Varying Delay”, IEEE Transactions on Neural Networks, vol. 21, no. 3, pp. 508-514, 2010.
• [16] Y. Zhao, L. Zhang, S. Shen and H. Gao, “Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks with Defective Statistics of Modes Transitions”, IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 164-170, 2011.
• [17] P. Balasubramaniam, S. Lakshmanan and R. Rakkiyappan, “Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties”, Neurocomputing, vol. 72, no. 16-18, pp. 3675-3682, 2009.
• [18] B. Kosko, “Adaptive bi-directional associative memories”, Appl. Opt., vol. 26, pp. 4947-4960, 1987.
• [19] G. Mathai, B.R. Upadhyaya, “Performance analysis and application of the bidirectional associative memoryto industrial spectral signatures”, Proc. IJCNN, vol. 89, no. 1, pp. 33-37, 1989.
• [20] S. Arik, “Global Asymptotic Stability Analysis of Bidirectional Associative Memory Neural Networks with Time Delays”, IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 580586, 2005.
• [21] JD. Cao, JL. Liang and J. Lam, “Exponential stability of high-order bidirectional associative memory neural networks with time delays”, Physica D-Nonlinear Phenomena, vol. 199, no. 3-4, pp. 425-436, 2004.
• [22] Z.-T. Huang, . X.-S Luo and Q.-G. Yang, “Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse”, Chaos, Solitons and Fractals, vol. 34, no. 3, pp. 878-885, 2007.
• [23] X. Lou, B. Cui and W. Wu, “On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reactiondiffusion terms”, Chaos, Solitons and Fractals, vol. 36, no. 4, pp. 1044-1054, 2008.
• [24] J.H. Park, S.M. Lee and O.M. Kwon, “On exponential stability of bidirectional associative memory neural networks with time-varying delays”, Chaos, Solitons and Fractals, vol. 39, pp. 10831091, 2009.
• [25] Y. Wang, “Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays”, Nonlinear Analysis: Real World Applications, vol. 10, pp. 1527-1539, 2009.
• [26] Y. Yuan and X. Li, “New results for global robust asymptotic stability of BAM neural networks with time-varying delays”, Neurocomputing, vol. 74, no. 1-3, pp. 337-342, 2010.
• [27] B. Chen, L. Yu and W.-A. Zhang , “Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays”, Neural Computing and Applications, vol. 20, no. 3, pp. 451-460, 2011.
• [28] P. Balasubramaniam and C. Vidhya, “Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms”, Journal of Computational and Applied Mathematics, vol. 234, no. 12, pp. 3458-3466, 2010.
• [29] Ju H. Park, C.H. Park, O.M. Kwon and S.M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type”, Applied Mathematics and Computation, vol. 199, no. 2, pp. 716-722, 2008.
• [30] Ju H. Park, “Robust stability of bidirectional associative memory neural networks with time delays”, Physics Letters A, vol. 349, no. 6, pp. 494-499, 2006.
• [31] X. F. Liao and K. Wong, “Global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays”, Physical Review E, vol. 67, no. 4, (0402901), 2003.
• [32] X. F. Liao and K. Wong, “Robust stability of interval bidirectional associative memory neural network with time delays”, IEEE Trans. Systems, Man and Cybernetics-Part C, vol. 34, pp. 1142-1154, 2004.
• [33] S. Senan and S. Arik, “New results for global robust stability of bidirectional associative memory neural networks with multiple time delays”, Chaos, Solitons and Fractals, vol. 41, no. 4, pp. 2106-2114, 2009.
• [34] S. Senan and S. Arik, “Global robust stability of bidirectional associative memory neural networks with multiple time delays”, IEEE Trans. Systems, Man and Cybernetics-Part B, vol. 37, no. 5, pp. 1375-1381, 2007.
• [35] N.Ozcan and S.Arik, “A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays”, Nonlinear Analysis:Real World Applications, vol.10, pp. 3312-3320, 2009.
• [36] O. Faydasicok and S. Arik, S. “ A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks”, Neural Networks, vol. 44, pp. 6471, 2013.
• [37] A. Chen, J. Cao and L. Huang, “Global robust stability of interval cellular neural networks with time-varying delays”, Chaos, Solitons and Fractals, vol. 23, no :3, pp. 787799, 2005.
• [38] T. Ensari and S. Arik, “New results for robust stability of dynamical neural networks with discrete time delays”, Expert Systems with Applications, vol. 37, no : 8, pp. 59255930, 2010.
• [39] V. Singh, “Global robust stability of delayed neural networks: estimating upper limit of norm of delayed connection weight matrix”, Chaos, Solitons and Fractals, vol. 32, no :1, pp. 259263, 2007.
• [40] S. Senan, S. Arik and D. Liu, “ New robust stability results for bidirectional associative memory neural networks with multiple time delays”, Applied Mathematics and Computation, vol. 218, no : 23, pp. 11472-11482, 2013.