Asymptotic stability criterion for fuzzy recurrent neural networks with interval time-varying delay. (English) Zbl 1494.93091
Balasubramaniam, P. (ed.) et al., Mathematical modelling and scientific computation. Proceedings of the 2nd international conference, ICMMSC 2012, Gandhigram, Tamil Nadu, India, March 16–18, 2012. Berlin: Springer. Commun. Comput. Inf. Sci. 283, 271-282 (2012).
Summary: This paper focuses on the delay-dependent asymptotic stability for fuzzy recurrent neural networks (FRNNs) with interval time-varying delay. The delay interval is decomposed into multiple uniform subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. By employing these LKFs, new delay-dependent asymptotic stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs), which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate the effectiveness of the proposed method.
For the entire collection see [Zbl 1242.00059].
For the entire collection see [Zbl 1242.00059].
MSC:
| 93D20 | Asymptotic stability in control theory |
| 34K20 | Stability theory of functional-differential equations |
| 93C42 | Fuzzy control/observation systems |
| 34K36 | Fuzzy functional-differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
Keywords:
fuzzy recurrent neural networks; interval time-varying delay; delay decomposition approach; linear matrix inequalities; maximum admissible upper bound (MAUB)References:
| [1] | Arik, S.: An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17, 1027-1031 (2004) · Zbl 1068.68118 · doi:10.1016/j.neunet.2004.02.001 |
| [2] | Mathiyalagan, K., Sakthivel, R., Anthoni, S.M.: New stability and stabilization criteria for fuzzy neural networks with various activation functions. Phys. Scr. 84, 015007 (2011) · Zbl 1219.82131 · doi:10.1088/0031-8949/84/01/015007 |
| [3] | Fang, Q., Tong, C.B., Yan, J.: A delay decomposition approach for stability of neural networks with time-varing delay. Chinese Phys. B 18, 5203 (2009) · doi:10.1088/1674-1056/18/12/017 |
| [4] | Song, Q., Cao, J.: Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time varying delays. IEEE Trans. Syst. Man Cybern. 37, 733-741 (2007) · doi:10.1109/TSMCB.2006.887951 |
| [5] | Ali, M.S., Balasubramaniam, P.: Stability analysis of uncertain fuzzy Hopfield neural networks with time delays. Commun. Nonlinear Sci. Numer. Simulat. 14, 2776-2783 (2009) · Zbl 1221.34191 · doi:10.1016/j.cnsns.2008.09.024 |
| [6] | Li, S., Goa, M., Yang, H.: Delay dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time varying delays. Fuzzy Sets Syst. 160, 3503-3517 (2009) · Zbl 1185.93109 · doi:10.1016/j.fss.2009.09.015 |
| [7] | Balasubramaniam, P., Chandran, R.: Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time varying delay. Commun. Nonlinear Sci. Numer. Simulat. 16, 2098-2108 (2011) · Zbl 1221.34214 · doi:10.1016/j.cnsns.2010.08.019 |
| [8] | Mahmoud, M.S., Xia, Y.: Improved exponential stability analysis for delayed recurrent neural networks. J. Franklin Inst. 348, 201-211 (2010) · Zbl 1214.34062 · doi:10.1016/j.jfranklin.2010.11.002 |
| [9] | Tian, J., Zhou, X.: Improved asymptotic stability criteria for neural networks with interval time varying delay. Expert Syst. Appl. 37, 7521-7525 (2010) · doi:10.1016/j.eswa.2010.04.093 |
| [10] | Li, C., Feng, G.: Delay-interval-dependent stability of recurrent neutral networks with e time varying delay. Neurocomputing 72, 1179-1183 (2009) · doi:10.1016/j.neucom.2008.02.011 |
| [11] | He, Y., Liu, G., Rees, D., Wu, M.: Stability analysis for neural networks with time-varying interval delay. IEEE Trans. Neural Netw. 18, 1850-1854 (2007) · doi:10.1109/TNN.2006.888373 |
| [12] | Chen, J., Sun, J., Liu, G.P., Rees, D.: New delay-dependent stability criteria for neural networks with time-varying interval delay. Physics Lett. A 374, 4397-4405 (2010) · Zbl 1238.82027 · doi:10.1016/j.physleta.2010.08.070 |
| [13] | Souza, F.O., Palhares, R.M.: Interval time-varying delay stability for neural networks. Neurocomputing 73, 2789-2792 (2010) · doi:10.1016/j.neucom.2010.04.002 |
| [14] | Takagi, T., Sugeno, M.: Fuzzy identification of system and its applications to modelling and control. IEEE. Trans. Syst. Man Cybern. 15, 116-132 (1985) · Zbl 0576.93021 · doi:10.1109/TSMC.1985.6313399 |
| [15] | Takagi, T., Sugeno, M.: Stability analysis and design of fuzzy control system. Fuzzy Sets Syst. 45, 135-156 (1992) · Zbl 0758.93042 · doi:10.1016/0165-0114(92)90113-I |
| [16] | Zhang, X.M., Han, Q.-L.: A delay decomposition approach to delay dependent stability for linear systems with time varying delays. Int. J. Robust Nonlinear Control 19, 1922-1930 (2009) · Zbl 1185.93106 · doi:10.1002/rnc.1413 |
| [17] | Xie, L.: Output feedback \(H_{ ∞ }\) control of systems with parameter uncertainty. Int. J. of Control 63, 741-750 (1996) · Zbl 0841.93014 · doi:10.1080/00207179608921866 |
| [18] | Han, Q.-L.: A new delay dependent stability creterion for linear neutral systems with norm-bounded uncertainities in all system matrices. Int. J. Syst. Sci. 36, 469-475 (2005) · Zbl 1093.34037 · doi:10.1080/00207720500157437 |
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.
