×

Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects. (English) Zbl 1398.93293

Summary: In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat’s lemma, Riemann-Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results.

MSC:

93D20 Asymptotic stability in control theory
68T05 Learning and adaptive systems in artificial intelligence
93C42 Fuzzy control/observation systems
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
Full Text: DOI

References:

[1] P. L. Butzer, U. Westphal, An Introduction to Fractional Calculus, 2000.; P. L. Butzer, U. Westphal, An Introduction to Fractional Calculus, 2000. · Zbl 0987.26005
[2] Podlubny, I., Fractional Differential Equations, (1999), Academic Press San Diego · Zbl 0918.34010
[3] Metzler, R.; Klafter, J., The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339, 1, 1-77, (2000) · Zbl 0984.82032
[4] Shimizuand, N.; Zhang, W., Fractional calculus approach to dynamic problems of viscoelastic materials, Int. J. Ser. C Mech. Syst. Mach. Elem. Manuf., 42, 4, 825-837, (1999)
[5] Baleanu, D., Fractional Dynamics and Control, (2012), Springer Berlin, Heidelberg
[6] Magin, R. L., Fractional calculus models of complex dynamics in biological tissues, Comput. Math. Appl., 59, 5, 1586-1593, (2010) · Zbl 1189.92007
[7] Kou, C.; Yan, Y.; Liu, J., Stability analysis for fractional differential equations and their applications in the models of HIV-1 infection, Comput. Model. Eng. Sci., 39, 3, 301, (2009) · Zbl 1257.92033
[8] Wu, H.; Zhang, X.; Xue, S., LMI conditions to global Mittag-Leffler stability of fractional-order neural networks with impulses, Neurocomputing, 193, 148-154, (2016)
[9] Stamov, G.; Stamova, I., Impulsive fractional-order neural networks with time-varying delays: almost periodic solutions, Neural Comput. Appl., 1-10, (2016)
[10] Wu, A.; Liu, L.; Huang, T., Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments, Neural Netw., 85, 118, (2016) · Zbl 1432.34102
[11] Chen, G.; Xia, J.; Zhuang, G., L2 gain analysis and state feedback stabilization of switched systems with multiple additive time-varying delays, J. Frankl. Inst., 354, 16, 7326-7345, (2017) · Zbl 1373.93257
[12] Wen, S.; Bao, G.; Zeng, Z.; Chen, Y.; Huang, T., Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 48, 195-203, (2013) · Zbl 1305.34129
[13] Li, X.; Song, S., Stabilization of delay systems: delay-dependent impulsive control, IEEE Trans. Autom. Control, 62, 1, 406-411, (2016) · Zbl 1359.34089
[14] Li, X.; Wu, J., Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica, 64, 63-69, (2016) · Zbl 1329.93108
[15] Li, C.; Yu, W.; Huang, T., Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach, Neural Netw., 54, 85-94, (2014) · Zbl 1307.93377
[16] Huang, T.; Li, C.; Duan, S.; Starzyk, J., Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects, IEEE Trans. Neural Netw. Learn. Syst., 23, 6, 866-875, (2012)
[17] Sun, G.; Zhang, Y., Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay, Neurocomputing, 131, 1, 323-330, (2014)
[18] W. Wang, Y. Cai, J. Li, Periodic behavior in a FIV model with seasonality as well as environment fluctuations,.(16) (2017) 7410-7428.; W. Wang, Y. Cai, J. Li, Periodic behavior in a FIV model with seasonality as well as environment fluctuations,.(16) (2017) 7410-7428. · Zbl 1373.93315
[19] Li, C.; Yu, X.; Huang, T.; Chen, G.; He, X., A generalized Hopfield network for nonsmooth constrained convex optimization: Lie derivative approach, IEEE Trans. Neural Netw. Learn. Syst., 27, 2, 308-321, (2015)
[20] Wen, S.; Zeng, Z.; Huang, T.; Meng, Q., Lag synchronization of switched neural networks via neural activation function and applications in image encryption, IEEE Trans. Neural Netw. Learn. Syst., 26, 7, 1493-1502, (2015)
[21] Yang, X.; Li, C.; Song, Q., Mittag-Leffler stability analysis on variable-time impulsive fractional-order neural networks, Neurocomputing, 207, 276-286, (2016)
[22] Yang, X.; Li, C.; Huang, T., Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses, Appl. Math. Computat., 293, 416-422, (2017) · Zbl 1411.34023
[23] Wu, R.; Dong, X.; Chen, L., Finite-time stability of fractional-order neural networks with delay, Commun. Theor. Phys., 60, 2, 189, (2013) · Zbl 1284.92016
[24] Yu, J.; Hu, C.; Jiang, H., Projective synchronization for fractional neural networks, Neural Netw., 49, 1, 87-95, (2014) · Zbl 1296.34133
[25] Stamova, I.; Stamov, G., Stability analysis of impulsive functional systems of fractional order, Commun. Nonlinear Sci. Numer. Simul., 19, 3, 702-709, (2014) · Zbl 1470.34202
[26] Zadeh, L. A., Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst., 90, 90, 111-127, (1997) · Zbl 0988.03040
[27] Bai, J.; Lu, R.; Xue, A., Finite-time stability analysis of discrete-time fuzzy Hopfield neural network, Neurocomputing, 159, 263-267, (2015)
[28] Balasubramaniam, P.; Vembarasan, V.; Rakkiyappan, R., Delay-dependent robust asymptotic state estimation of Takagi-sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays, Expert Syst. Appl., 39, 1, 472-481, (2012)
[29] Zadeh, L. A., The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets Syst., 11, 1, 197-198, (1983) · Zbl 0553.68049
[30] Lee, C. C., Fuzzy logic in control systems, IEEE Trans. Syst. Man Cybern., 20, 2, 419-435, (1990) · Zbl 0707.93037
[31] Arunkumar, A.; Sakthivel, R.; Mathiyalagan, K., Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks, ISA Trans., 53, 4, 1006-1014, (2014)
[32] Huang, T., Robust stability of delayed fuzzy Cohen-Grossberg neural networks, Comput. Math. Appl., 61, 8, 2247-2250, (2011) · Zbl 1219.93094
[33] Balasubramaniam, P.; Vidhya, C., Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters, Expert Syst. Appl., 39, 3, 3109-3115, (2012)
[34] Kao, Y.; Shi, L.; Xie, J., Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability, Neural Netw., 63, 18-30, (2015) · Zbl 1328.34078
[35] Ding, W.; Han, M.; Li, M., Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses, Phys. Lett. A, 373, 8, 832-837, (2009) · Zbl 1228.34075
[36] Gan, Q.; Xu, R.; Yang, P., Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion, Commun. Nonlinear Sci. Numer. Simul., 17, 4, 1862-1870, (2012) · Zbl 1239.93110
[37] Chen, J.; Zeng, Z.; Jiang, P., Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks, Neural Netw., 51, 3, 1-8, (2014) · Zbl 1306.34006
[38] Chen, B.; Chen, J., Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks, Neural Netw., 68, 78, (2015) · Zbl 1398.34014
[39] Alofi, A.; Cao, J.; Elaiw, A., Delay-dependent stability criterion of Caputo fractional neural networks with distributed delay, Discret. Dyn. Nat. Soc., 2014, 1, 1-6, (2014) · Zbl 1418.92005
[40] Chen, L.; Chai, Y.; Wu, R., Dynamic analysis of a class of fractional-order neural networks with delay, Neurocomputing, 111, 6, 190-194, (2013)
[41] Chen, L.; Qu, J.; Chai, Y., Synchronization of a class of fractional-order chaotic neural networks, Entropy, 15, 8, 3265-3276, (2013) · Zbl 1339.34060
[42] Subramanian, K.; Savitha, R.; Suresh, S., A complex-valued neuro-fuzzy inference system and its learning mechanism, Neurocomputing, 123, 110-120, (2014)
[43] Wu, A.; Zeng, Z., Boundedness, Mittag-Leffler stability and asymptotical ω-periodicity of fractional-order fuzzy neural networks, Neural Netw., 74, 73-84, (2016) · Zbl 1398.34011
[44] Slotine, J.; Li, W., Applied Nonlinear Control, (1991), Prentice-Hall Englewood Cliffs. NJ · Zbl 0753.93036
[45] Li, C.; Deng, W., Remarks on fractional derivatives, Appl. Math. Comput., 187, 2, 777-784, (2007) · Zbl 1125.26009
[46] Wang, F.; Yang, Y.; Hu, M., Asymptotic stability of delayed fractional-order neural networks with impulsive effects, Neurocomputing, 154, 239-244, (2015)
[47] Yang, T.; Yang, L. B., The global stability of fuzzy cellular neural network, IEEE Tran. Circuits Syst. I Fundam. Theory Appl., 43, 10, 880-883, (1996)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.