Abstract
In this paper, the delay-dependent stability problem for a class of neural networks of neutral-type with interval time-varying delays and nonlinear perturbations is investigated. A novel stability criterion is obtained in terms of linear matrix inequality (LMI) by employing a Lyapunov-Krasovskii functional. The proposed criteria can be checked easily by the LMI Control Toolbox in Matlab. In addition, two examples are given to show the effectiveness of the obtained result.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sun, C.Y., Zhang, K.J., Fei, S.M., Feng, C.: On exponential stability of delayed neural networks with a general class of activation functions. Physics Letters A 298, 122–132 (2002)
Zhang, Q., Ma, R.N., Chao, W., Jin, X.: On the global stability of delayed neural networks. IEEE Trans on Automatic Control 48(5), 794–7973 (2003)
Sun, C.Y., Feng, C.B.: Exponential periodicity and stability of delayed neural networks. Mathematics and Computers in Simulation 66(6), 469–478 (2004)
Liao, X.F., Li, C.D.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D-Nonlinear Phenomena 200, 139–155 (2005)
Zhang, Q., Wei, X.P., Xu, J.: On global exponential stability of nonautonomous delayed neural networks. Chaos Soliton Fract. 26(3), 965–970 (2005)
Shen, T., Zhang, Y.: Improved global robust stability criteria for delayed neural networks. IEEE Trans. on Circuits and Systems Ii-Express Briefs 54(8), 715–719 (2007)
Wu, W., Cui, B.T.: Improved sufficient conditions for global asymptotic stability of delayed neural networks. IEEE Trans. on Circuits and Systems Ii-Express Briefs 54(7), 626–630 (2007)
Zhang, Q., Wei, X.P., Xu, J.: A new global stability result for delayed neural networks. Nonlinear Anal.-Real. 8(3), 1024–1028 (2007)
Wu, W., Cui, B.T.: Global robust exponential stability of delayed neural networks. Chaos Soliton Fract. 35(4), 747–754 (2008)
Sun, Y.H., Cao, J.D.: Novel criteria for mean square stability of stochastic delayed neural networks. Neural Network World 18(3), 245–254 (2008)
Yucel, E., Arik, S.: Novel results for global robust stability of delayed neural networks. Chaos Soliton Fract. 39(4), 1604–1614 (2009)
Hu, C., Jiang, H.J., Teng, Z.D.: Globally Exponential Stability for Delayed Neural Networks under Impulsive Control. Neural Process. Lett. 31(2), 105–127 (2010)
Cheng, C.J., Liao, T.L., Yan, J.J., Hwang, C.C.: Globally asymptotic stability of a class of neutral-type neural networks with delays. IEEE Trans. Syst Man Cybern. B Cybern. 36(5), 1191–1195 (2006)
He, H.L., Liao, X.X.: Stability analysis of neutral neural networks with time delay. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 147–152. Springer, Heidelberg (2006)
Park, J.H., Kwon, O.M.: Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208(1), 69–75 (2009)
Liu, J., Zong, G.D.: New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type. Neurocomputing 72, 2549–2555 (2009)
Park, J.H., Kwon, O.M.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202(1), 360–369 (2008)
Wu, H.L., Zhong, Y., Mai, H.H.: On Delay-dependent Exponential Stability of Neutral-type Neural Networks with Interval Time-varying Delays. In: Proceedings of 2009 International Conference on Artificial Intelligence and Computational Intelligence, vol. Ii, pp. 563–569 (2009)
Park, J.H., Kwon, O.M.: Global stability for neural networks of neutral-type with interval time-varying delays. Chaos Soliton Fract. 41(3), 1174–1181 (2009)
Lien, C.H., Yu, K.W., Lin, Y.F., Chung, Y.J., Chung, L.: Exponential convergence rate estimation for uncertain delayed neural networks of neutral type. Chaos Soliton Fract. 40(5), 2491–2499 (2009)
Mahmoud, M.S., Ismail, A.: Improved results on robust exponential stability criteria for neutral-type delayed neural networks. Appl. Math. Comput. 217(7), 3011–3019 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, G., Yang, S.X., Fu, W. (2011). Delay-Dependent Stability Criterion for Neural Networks of Neutral-Type with Interval Time-Varying Delays and Nonlinear Perturbations. In: Tan, Y., Shi, Y., Chai, Y., Wang, G. (eds) Advances in Swarm Intelligence. ICSI 2011. Lecture Notes in Computer Science, vol 6728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21515-5_55
Download citation
DOI: https://doi.org/10.1007/978-3-642-21515-5_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21514-8
Online ISBN: 978-3-642-21515-5
eBook Packages: Computer ScienceComputer Science (R0)