×

zbMATH — the first resource for mathematics

Stability analysis of fuzzy Markovian jumping Cohen-Grossberg BAM neural networks with mixed time-varying delays. (English) Zbl 1221.34201
Summary: We investigate the robust stability of uncertain fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. A new delay-dependent stability condition is derived under uncertain switching probabilities by Takagi–Sugeno fuzzy model. Based on the Linear Matrix Inequality (LMI) technique, upper bounds for the discrete and distributed delays are calculated using the LMI toolbox in MATLAB. Numerical examples are provided to illustrate the effectiveness of the proposed method.

MSC:
34K20 Stability theory of functional-differential equations
34K36 Fuzzy functional-differential equations
60J28 Applications of continuous-time Markov processes on discrete state spaces
92B20 Neural networks for/in biological studies, artificial life and related topics
Software:
LMI toolbox; Matlab
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cohen, M.A.; Grossberg, S., Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE trans syst man cybernet B, 13, 815-826, (1983) · Zbl 0553.92009
[2] Gu, K.; Kharitonov, V.; Chen, J., Stability of time delay systems, (2003), Birkhuser Boston · Zbl 1039.34067
[3] Chen, T.; Rong, L., Delay-independent stability analysis of cohen – grossberg neural networks, Phys lett A, 317, 436-449, (2003) · Zbl 1030.92002
[4] Arik, S.; Orman, Z., Global stability analysis of cohen – grossberg neural networks with time-varying delays, Phys lett A, 341, 410-421, (2005) · Zbl 1171.37337
[5] Yuan, K.; Cao, J., An analysis of global asymptotic stability of delayed cohen – grossberg neural networks via nonsmooth analysis, IEEE trans circuits syst I, regular papers, 52, 1854-1861, (2005) · Zbl 1374.34291
[6] Rong, L.B., LMI-based criteria for robust stability of cohen – grossberg neural networks with delays, Phys lett A, 339, 63-73, (2005) · Zbl 1137.93401
[7] Wu, W.; Cui, B.T.; Lou, X.Y., Some criteria for asymptotic stability of cohen – grossberg neural networks with time varying delays, Neurocomputing, 70, 1085-1088, (2007)
[8] Xiong, W.; Xu, B., Some criteria for robust stability of cohen – grossberg neural networks with delays, Chaos soliton fract, 36, 1357-1365, (2008) · Zbl 1183.34074
[9] Ji, C.; Zhang, H.G.; Wei, Y., LMI approach for global robust stability of cohen – grossberg neural networks with multiple delays, Neurocomputing, 71, 475-485, (2008)
[10] Sing, V., Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEE proc control theory appl, 151, 125-129, (2004)
[11] Song, Q.K.; Cao, J.D., Stability analysis of cohen – grossberg neural networks with both time-varying and continuously distributed delays, J comput appl math, 197, 188-203, (2006) · Zbl 1108.34060
[12] Li, T.; Fei, S.M., Stability analysis of cohen – grossberg neural networks with time-varying and distributed delays, Neurocomputing, 71, 1069-1081, (2008)
[13] Su, W.W.; Chen, Y.M., Global robust stability criteria of stchastic cohen – grossberg neural networks with discrete and distributed delays, Commun nonlinear sci numer simul, 14, 520-528, (2009) · Zbl 1221.37196
[14] Liu, Y.R.; Wang, Z.D.; Liu, X.H., On global exponential stability of generalized stochastic neural networks with mixed time-delays, Neurocomputing, 70, 314-326, (2006)
[15] Li, T.; Song, A.G.; Fei, S.M., Robust stability of stochastic cohen – grossberg neural networks with mixed time-varying delays, Neurocomputing, 73, 542-551, (2009)
[16] Fu, X.; Li, X., LMI conditions for stability of impulsive stochastic cohen – grossberg neural networks with mixed delays, Commun nonlinear sci numer simul, 16, 435-454, (2011) · Zbl 1221.34195
[17] Mariton, M., Jump linear control system, (1990), Marcel-Dekker New York · Zbl 0628.93074
[18] Wang, Z.; Liu, Y.; Yu, L.; Liu, X., Exponenetial stability of delayed recurrent neural networks with Markovian jumping parameters, Phys lett A, 356, 346-352, (2006) · Zbl 1160.37439
[19] Gao, M.; Cui, B.; Lou, X., Robust exponenetial stability of Markovian jumping neural networks with time-varying delay, Int J neural syst, 18, 207-218, (2008)
[20] Zhang, H.; Wang, Y., Stability analysis of Markovian jumping stochastic cohen – grossberg neural networks with mixed time delays, IEEE trans neural networks, 19, 366-370, (2008)
[21] Balasubramaniam, P.; Rakkiyappan, R., Delay-dependent robust stability analysis for Markovian jumping stochastic cohen – grossberg neural networks with discrete interval and distributed time-varying delays, Nonlinear anal: hybrid syst, 3, 207-214, (2009) · Zbl 1184.93093
[22] Sheng, L.; Yang, H., Robust stability of uncertain Markovian jumping cohen – grossberg neural networks with mixed time-varying delays, Chaos soliton fract, 42, 2120-2128, (2009) · Zbl 1198.93166
[23] Kosko, B., Adaptive bi-directional associative memories, Appl opt, 26, 4947-4960, (1987)
[24] Kosko, B., Bi-directional associative memories, IEEE trans syst man cybernet B, 18, 49-60, (1988)
[25] Kosko B. Neural networks and fuzzy systems – a dynamical system approach to machine intelligence. Englewood Cliffs, NJ: Prentice Hall; 1992. · Zbl 0755.94024
[26] Lou, X.Y.; Cui, B.T., Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE trans syst man cybernet B, 37, 713-719, (2007)
[27] Liu, H.; Ou, Y.; Hu, J.; Liu, T., Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters, Neural networks, 23, 315-321, (2010) · Zbl 1400.34117
[28] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE trans syst man cybernet B, 15, 116-132, (1985) · Zbl 0576.93021
[29] Cao, Y.Y.; Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE trans fuzzy syst, 8, 200-211, (2000)
[30] Cao, Y.Y.; Frank, P.M., Stability analysis and synthesis of nonlinear time-delay systems via linear takagi – sugeno fuzzy models, Fuzzy sets syst, 124, 213-229, (2001) · Zbl 1002.93051
[31] Zhang, Y.; Heng, P.A., Stability of fuzzy control systems with bounded uncertain delays, IEEE trans fuzzy syst, 10, 92-97, (2002) · Zbl 1142.93377
[32] Lin, F.J.; Wai, R.J., Robust recurrent fuzzy neural network control for linear synchronous motor drive system, Neurocomputing, 50, 365-390, (2003) · Zbl 1006.68824
[33] Lou, X.Y.; Cui, B.T., Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays, Fuzzy sets syst, 158, 2746-2756, (2007) · Zbl 1133.93366
[34] Wu, H.N.; Cai, K.Y., Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control, IEEE trans syst man cybernet B, 36, 509-519, (2006)
[35] Zhang, J.; Ren, D.; Zhang, W., Global exponential stability of fuzzy cohen – grossberg neural networks with variable delays and distributed delays, Lecture notes comput sci, 66-74, (2007)
[36] Li, H.; Chen, B.; Zhou, Q.; Qian, W., Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters, IEEE trans syst man cybernet B, 39, 94-102, (2009)
[37] Feng, C.; Plamondon, R., Stability analysis of bi-directional associative memory networks with time delays, IEEE trans neural networks, 14, 1560-1565, (2003)
[38] Li, Y.; Chen, X.; Zhao, L., Stability and existence of periodic solutions to delayed cohen – grossberg BAM neural networks with impulses on time scales, Neurocomputing, 72, 1621-1630, (2009)
[39] Xi, H.; Cao, J., Exponential stability of periodic solution to cohen – grossberg-type BAM networks with time-varying delays, Neurocomputing, 72, 1702-1711, (2009)
[40] Li, X., Existence and global exponential stability of periodic solution for impulsive cohen – grossberg-type BAM neural networks with continuously distributed delays, Appl math comput, 215, 292-307, (2009) · Zbl 1190.34093
[41] Li, X., Exponential stability of cohen – grossberg-type BAM neural networks with time-varying delays via impulsive control, Neurocomputing, 73, 525-530, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.