×

Global robust point dissipativity of interval neural networks with mixed time-varying delays. (English) Zbl 1169.92005

Summary: The global robust point dissipativity of an uncertain neural network model with mixed time-varying delays is investigated, based on Lyapunov theory and inequality techniques. First, the concept of global robust point dissipativity is introduced. Next, some sufficient conditions are given for checking the global robust point dissipativity and the global exponential robust dissipativity of the uncertain neural networks model. Finally, illustrative examples are given to show the efficiency of our results.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Takahashi, N.: A new sufficient condition for complete stability of cellular neural networks with delay. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47, 793–799 (2000) · Zbl 0964.94008 · doi:10.1109/81.852931
[2] Joy, M.: Results concerning the absolute stability of delayed neural networks. Neural Netw. 13, 613–616 (2000) · doi:10.1016/S0893-6080(00)00042-3
[3] Cheng, C., Liao, T., Yan, J., Hwang, C.: Correspondence globally asymptotic stability of a class of neutral-type neural networks with delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 36, 1191–1195 (2006) · doi:10.1109/TSMCB.2006.874677
[4] Chen, A., Cao, J., Huang, L.: An estimation of upper bound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49, 1028–1032 (2000) · Zbl 1368.93462 · doi:10.1109/TCSI.2002.800841
[5] He, Y., Wu, M., She, J.: Delay-dependent exponential stability of delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. II Express Briefs 53, 553–557 (2006) · doi:10.1109/TCSII.2006.883209
[6] Zeng, Z., Wang, J., Liao, X.: Global exponential stability of a general class of recurrent networks with time-varying delays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50, 1353–1358 (2003) · Zbl 1368.34089 · doi:10.1109/TCSI.2003.817760
[7] Cao, J., Wang, L.: Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Netw. 13, 457–463 (2002) · doi:10.1109/72.991431
[8] Cao, J., Wang, J.: Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw. 17, 379–390 (2004) · Zbl 1074.68049 · doi:10.1016/j.neunet.2003.08.007
[9] Cao, J.: Global stability conditions for delayed CNNs. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48, 1330–1333 (2001) · Zbl 1006.34070 · doi:10.1109/81.964422
[10] Feng, C., Plamondon, R.: On the stability analysis of delayed neural networks systems. Neural Netw. 14, 1181–1188 (2001) · Zbl 02022184 · doi:10.1016/S0893-6080(01)00088-0
[11] He, Y., Wanga, Q., Wu, M.: LMI-based stability criteria for neural networks with multiple time-varying delays. Physica D 212, 126–136 (2005) · Zbl 1097.34054 · doi:10.1016/j.physd.2005.09.013
[12] Cao, J., Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 52, 417–426 (2005) · Zbl 1374.93285 · doi:10.1109/TCSI.2004.841574
[13] Zhang, J.: Global exponential stability of interval neural networks with variable delays. Appl. Math. Lett. 19, 1222–1227 (2006) · Zbl 1180.34083 · doi:10.1016/j.aml.2006.01.005
[14] Yang, X., Liao, X., Bai, S., Jevans, D.: Robust exponential stability and domains of attraction in a class of interval neural networks. Chaos Solitons Fractals 26, 445–451 (2005) · Zbl 1112.34326 · doi:10.1016/j.chaos.2004.12.041
[15] Singh, V.: On global robust stability of interval Hopfield neural networks with delay. Chaos Solitons Fractals 33, 1183–1188 (2007) · Zbl 1151.34333 · doi:10.1016/j.chaos.2006.01.121
[16] Cao, J., Li, H., Han, L.: Novel results concerning global robust stability of delayed neural networks. Real World Appl. 7, 458–469 (2006) · Zbl 1102.92001 · doi:10.1016/j.nonrwa.2005.03.012
[17] He, Y., Wang, Q., Zheng, W.: Global robust stability for delayed neural networks with polytopic type uncertainties. Chaos Solitons Fractals 26, 1349–1354 (2005) · Zbl 1083.34535 · doi:10.1016/j.chaos.2005.04.005
[18] Wang, M., Wang, L.: Global asymptotic robust stability of static neural network models with S-type distributed delays. Math. Comput. Model. 44, 218–222 (2006) · Zbl 1139.93023 · doi:10.1016/j.mcm.2006.01.013
[19] Cao, J., Yuan, K., Ho, D.W.C., Lam, J.: Global point dissipativity of neural networks with mixed time-varying delays. Chaos 16, 013105 (2006) · Zbl 1144.37332 · doi:10.1063/1.2126940
[20] Masubuchi, I.: Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains. Syst. Control Lett. 55, 158–164 (2006) · Zbl 1129.93475 · doi:10.1016/j.sysconle.2005.06.007
[21] Song, Q., Zhao, Z.: Global dissipativity of neural networks with both variable and unbounded delays. Chaos Solitons Fractals 25, 393–401 (2005) · Zbl 1072.92005 · doi:10.1016/j.chaos.2004.11.035
[22] Arik, S.: On the global dissipativity of dynamical neural networks with time delays. Phys. Lett. A 326, 126–132 (2004) · Zbl 1161.37362 · doi:10.1016/j.physleta.2004.04.023
[23] Liao, X., Wang, J.: Global dissipativity of continuous-time recurrent neural networks with time delay. Phys. Rev. E 68, 016118 (2003) · doi:10.1103/PhysRevE.68.016118
[24] Guo, L., Wang, H.: Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters. IEEE Trans. Circuit Syst.-I 52, 1644–1652 (2005) · Zbl 1374.94963 · doi:10.1109/TCSI.2005.851686
[25] Guo, L., Wang, H.: Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises. IEEE Trans. Automat. Contr. 51 695–700 (2006) · Zbl 1366.93655 · doi:10.1109/TAC.2006.872771
[26] Gu, K., Kharitonov, V., Chen, J.: Stability of Time-delay Systems. Birkhauser, Boston (2003) · Zbl 1039.34067
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.