TY - JOUR T1 - Stability Analysis of A Class of Takagı-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Time Delays TT - TAKAGİ-SUGENO BULANIK COHEN-GROSSBERG TİPİ ZAMAN GECİKMELİ YAPAY SİNİR AĞLARINDA KARARLILIK ANALİZİ AU - Özcan Semerci, Neyir AU - Barış, Samet PY - 2018 DA - August Y2 - 2018 DO - 10.17482/uumfd.406443 JF - Uludağ Üniversitesi Mühendislik Fakültesi Dergisi JO - UUJFE PB - Bursa Uludağ Üniversitesi WT - DergiPark SN - 2148-4155 SP - 45 EP - 54 VL - 23 IS - 2 LA - en AB - This paper deals with the problem of the globalasymptotic stability of the class of Takagi-Sugeno Fuzzy Cohen-Grossberg neuralnetworks with multiple time delays. By constructing a suitable fuzzy Lyapunovfunctional, we present a new delay-independent sufficient condition for theglobal asymptotic stability of the equilibrium point for delayed Takagi-SugenoFuzzy Cohen-Grossberg neural networks with respect to the Lipschitz activationfunctions. The obtained condition simply relies on the network parameters of theneural system. Therefore, the equilibrium and stability properties of theneural network model considered in this paper can be easily verified byexploiting some basic properties of some certain classes of matrices. KW - T-S Fuzzy Neural Networks KW - Delayed Systems KW - Lyapunov Functionals N2 - Bu çalışma çoklu zaman gecikmeli Takagi-Sugeno BulanıkCohen-Grossberg tipi yapay sinir ağlarının global asimtotik kararlılık problemiile ilgilenmektedir. Uygun bulanık Lyapunov fonksiyonelleri kullanılarak veaktivasyon fonksiyonlarının Lipschitz olduğu dikkate alnarak, gecikmeli Takagi-SugenoBulanık Cohen-Grossberg yapay sinir ağlarında denge noktasının global asimtotikgecikme parametrelerinden bağımsız olarak, yeni yeterli bir kararlılık koşulusunulmuştur. Elde edilen koşul sadece sinir ağının sistem parametrelerine bağlıolarak ifade edilmiştir. Bu nedenle, bu çalışmada çalışılan yapay sinir ağı modelinin denge ve kararlılıközellikleri, bazı özel matris sınıflarının temel özellikleri kullanarak kolaylıkladoğrulanabilir. CR - Ahn, C. K. (2011) Takagi-Sugeno fuzzy Hopfield neural networks for H-infinity nonlinear system identification, Neural Processing Letters, 34(1), 59-70. doi: 10.1007/s11063-011-9183-z CR - Arik, S. and Orman, Z. (2005) Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Physics Letters A, 341(5-6), 410-421. doi:10.1016/j.physleta.2005.04.095 CR - Balasubramaniam, P. and Ali, M. S. (2011) Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays, Mathematical and Computer Modelling, 53(1-2), 151-160. doi:10.1016/j.mcm.2010.07.028 CR - Bao, G., Wen, S. and Zeng, Z. (2012) Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Networks, 33, 32-41. doi:10.1016/j.neunet.2012.04.003 CR - Bao, H. (2016) Existence and exponential stability of periodic solution for BAM fuzzy Cohen-Grossberg neural networks with mixed delays, Neural Processing Letters, 43(3), 871-885. doi: 10.1007/s11063-015-9455-0 CR - Chandran, R. and Balasubramaniam, P. (2013) Delay dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay, Neural Processing Letters, 37(2), 147-161. doi: 10.1007/s11063-012-9239-8 CR - Cohen, M.A. and Grossberg, S. (1983) Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Transactions on Systems, Man and Cybernetics, 13(5), 815-821. CR - Gan, Q., Xu, R. and Yang, P. (2010) Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms, Neural Processing Letters, 32(1), 45-57. doi: 10.1007/s11063-010-9144-y CR - Gan, Q. (2013) Exponential synchronization of stochastic fuzzy cellular neural networks with reaction-diffusion terms via periodically intermittent control, Neural Processing Letters, 37(3), 393-410. doi: 10.1007/s11063-012-9254-9 CR - He, D. and Xu, D. (2008) Attracting and invariant sets of fuzzy Cohen-Grossberg neural networks with time-varying delays, Physics Letters A, 372(47), 7057-7062. doi:10.1016/j.physleta.2008.10.035 CR - Hou, Y.Y, Liao, T.L. and Yan, J.J. (2007) Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays, IEEE Transactions on Systems, Man and Cybernetics, 37(3), 720-726. doi: 10.1109/TSMCB.2006.889628 CR - Huang, H., Ho, D.W.C. and Lam, J. (2005) Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Transactions on Circuits Systems-I, Fundamental Theory and Applications, 52(5), 251-255. doi: 10.1109/TCSII.2005.846305 CR - Jian, J. and Jiang, W. (2017) Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays, Fuzzy Sets and Systems, 277, 65-80. doi: 10.1016/j.fss.2014.12.006 CR - Li, C., Li, Y. and Ye, Y. (2010) Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, 15(11), 3599-3606. doi:10.1016/j.cnsns.2010.01.001 CR - Mathiyalagan, K., Park, J. H., Sakthivel, R. and Anthoni, S. M. (2014) Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks, Applied Mathematics and Computation, 230, 451-463. doi: 10.1016/j.amc.2013.12.063 CR - Nie, X., Zheng, W. X. and Cao, J. (2015) Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays, Neural Networks, 71, 27-36. doi: 10.1016/j.neunet.2015.07.009 CR - Senan, S. (2018) An analysis of global stability of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with time delays, Neural Processing Letters, https://doi.org/10.1007/s11063-018-9792-x. CR - Takagi, T. and Sugeno, M. (1985) Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, 15(1), 116-132. CR - Tseng, K.H, Tsai, J. S. and Lu, C. Y. (2012) Design of delay-dependent exponential estimator for T-S Fuzzy Neural networks with mixed time-varying interval delays using hybrid Taguchi-Genetic algorithm, Neural Processing Letters, 36(1), 49-67. doi: 10.1007/s11063-012-9222-4 CR - Xie, W. and Zhu, Q. (2015) Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients, Neurocomputing, 166, 133-139. doi: 10.1016/j.neucom.2015.04.020 CR - Yamamoto, H. and Furuhashi, T. (2001) A new sufficient condition for stable fuzzy control system and its design method, IEEE Transactions on Fuzzy Systems, 9(4), 554-569. CR - Yang, W. (2014) Periodic solution for fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients, Neural Processing Letters, 40(1), 51-73. doi: 10.1007/s11063-013-9310-0 CR - Zheng, C.D., Shan, Q. H., Zhang, H. and Wang, Z. (2013) On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching, IEEE Transactions on Neural Networks and Learning Systems, 24(5), 800-811. doi: 10.1109/TNNLS.2013.2244613 CR - Zheng, C. D., Zhang, X. and Wang, Z. (2016) Mode and delay-dependent stochastic stability conditions of fuzzy neural networks with Markovian jump parameters, Neural Processing Letters, 43(1), 195-217. doi: 10.1007/s11063-015-9413-x UR - https://doi.org/10.17482/uumfd.406443 L1 - https://dergipark.org.tr/tr/download/article-file/498857 ER -