# zbMATH — the first resource for mathematics

Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks. (English) Zbl 1410.93071
Summary: In this paper, the problem of robust exponential stability analysis for a class of Takagi-Sugeno (TS) fuzzy Cohen-Grossberg neural networks with uncertainties and time-varying delays is investigated. A generalized activation function is used, and the assumptions such as boundedness, monotony and differentiability of the activation functions are removed. By using a Lyapunov-Krasovskii functional and employing the delay fractioning approach, a set of sufficient conditions are established for achieving the required result. The obtained conditions are proposed in terms of linear matrix inequalities (LMIs), so its feasibility can be checked easily via standard numerical toolboxs. The main advantage of the proposed criteria lies in its reduced conservatism which is mainly based on the time delay fractioning technique. In addition to that, a numerical example with simulation results is given to show the effectiveness of the obtained LMI conditions.

##### MSC:
 93C42 Fuzzy control/observation systems 93D09 Robust stability 92B20 Neural networks for/in biological studies, artificial life and related topics 34K20 Stability theory of functional-differential equations
Full Text:
##### References:
 [1] Boyd, S.; Ghoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA [2] Chen, Y., Global asymptotic stability of delayed Cohen-Grossberg neural networks, IEEE Trans. Circuits Syst. I, 53, 2, 351-357, (2006) · Zbl 1374.82019 [3] Cohen, M. A.; Grossberg, S., Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst. Man Cybern., 13, 815-826, (1983) · Zbl 0553.92009 [4] Faydasicok, O.; Arik, S., A new robust stability criterion for dynamical neural networks with multiple time delays, Neurocomputing, 99, 290-297, (2013) [5] Hu, L.; Gao, H.; Zheng, W. X., Novel stability of cellular neural networks with interval time-varying delay, Neural Netw., 21, 1458-1463, (2008) · Zbl 1254.34102 [6] Huang, T., Robust stability of delayed fuzzy Cohen-Grossberg neural networks, Comput. Math. Appl., 61, 2247-2250, (2011) · Zbl 1219.93094 [7] Kwon, O. M.; Lee, S. M.; Park, J. H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Appl. Math. Comput., 218, 9953-9964, (2012) · Zbl 1253.34066 [8] Kwon, O. M.; Park, J. H., Improved delay-dependent stability criterion for neural networks with time-varying delays, Phys. Lett. A, 373, 529-535, (2009) · Zbl 1227.34030 [9] S. Lakshmanan, K. Mathiyalagan, J.H. Park, R. Sakthivel, F.A. Rihan, Delay-dependent $$H_\infty$$ state estimation of neural networks with mixed time-varying delays, Neurocomputing, 2013. DOI: g/10.1016/j.neucom.2013.09.020/i. [10] Lakshmanan, S.; Rakkiyappan, R.; Balasubramaniam, P., Global robust stability criteria for T-S fuzzy systems with distributed delays and time-delay in the leakage term, Iran. J. Fuzzy Syst., 9, 127-146, (2012) · Zbl 1260.93101 [11] Li, C.; Li, Y.; Ye, Y., Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Commun. Nonlinear Sci. Numer. Simul., 15, 3599-3606, (2010) · Zbl 1222.34090 [12] Liu, Q.; Xu, R., Stability and bifurcation of a Cohen-Grossberg neural network with discrete delays, Appl. Math. Comput., 218, 2850-2862, (2011) · Zbl 1283.34065 [13] Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Netw., 19, 667-675, (2006) · Zbl 1102.68569 [14] Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S., New stability and stabilization criteria for fuzzy neural networks with various activation functions, Phys. Scr., 84, 015007, (2011) · Zbl 1219.82131 [15] Mou, S.; Gao, H.; Qiang, W.; Chen, K., New delay-dependent exponential stability for neural networks with time delay, IEEE Trans. Syst. Man Cybern., 38, 571-576, (2008) [16] Park, J. H.; Park, C. H.; Kwon, O. M.; Lee, S. M., A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199, 716-722, (2008) · Zbl 1149.34345 [17] Park, J. H., Further note on global exponential stability of uncertain cellular neural networks with variable delays, Appl. Math. Comput., 188, 850-854, (2007) · Zbl 1126.34376 [18] Park, J. H., A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos Solitons Fractals, 29, 446-453, (2006) · Zbl 1121.92006 [19] Park, J. H., Synchronization of cellular neural networks of neutral type via dynamic feedback controller, Chaos Solitons Fractals, 42, 1299-1304, (2009) · Zbl 1198.93182 [20] Rakkiyappan, R.; Balasubramaniam, P., On exponential stability results for fuzzy impulsive neural networks, Fuzzy Sets Syst., 161, 1823-1835, (2010) · Zbl 1198.34160 [21] Sakthivel, R.; Arunkumar, A.; Mathiyalagan, K.; Marshal Anthoni, S., Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays, Appl. Math. Comput., 218, 3799-3809, (2011) · Zbl 1257.34059 [22] Sakthivel, R.; Mathiyalagan, K.; Marshal Anthoni, S., Design of controller on passification for uncertain fuzzy Hopfield neural networks with time-varying delays, Phys. Scr., 84, 045024, (2011) · Zbl 1263.34117 [23] Sakthivel, R.; Samidurai, R.; Marshal Anthoni, S., New exponential stability criteria for stochastic BAM neural networks with impulses, Phys. Scr., 82, 045802, (2010) · Zbl 1202.93101 [24] Bao, G.; Wen, S.; Zeng, Z., Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Netw., 33, 32-41, (2012) · Zbl 1267.34137 [25] Zhu, Q.; Li, X., Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, Fuzzy Sets Syst., 203, 74-94, (2012) · Zbl 1253.93135 [26] Song, Q., Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach, Neurocomputing, 71, 2823-2830, (2008) [27] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 116-132, (1985) · Zbl 0576.93021 [28] Wang, C.; Li, Y., Existence and stability analysis of discrete-time fuzzy BAM neural networks with delays and impulses, World Acad. Sci. Eng. Tech., 55, 1122-1131, (2011) [29] Wang, Y.; Wang, Z.; Liang, J., A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances, Phys. Lett. A, 372, 6066-6073, (2008) · Zbl 1223.90013 [30] Wang, Z.; Shu, H.; Fang, J.; Liu, X., Robust stability for stochastic Hopfield neural networks with time delays, Nonlinear Anal. Real World Appl., 7, 1119-1128, (2006) · Zbl 1122.34065 [31] Zhang, Q.; Xiang, R., Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Phys. Lett. A, 372, 3971-3977, (2008) · Zbl 1220.34098 [32] Zhang, Z.; Liu, W.; Zhou, D., Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays, Neural Netw., 25, 94-105, (2012) · Zbl 1266.34124
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.