Abstract
The problem of global robust exponential stability in Lagrange sense for the interval delayed neural networks (IDNNs) with general activation functions is investigated. Based on the Lyapunov stability, a differential inequality and linear matrix inequalities (LMIs) technique, some conditions to guarantee the IDNNs global exponential stability in Lagrange sense are provided. Meanwhile, the specific estimation of globally exponentially attractive sets of the addressed system are also derived. Finally, a numerical example is provided to illustrate the effectiveness of the method proposed.
This is a preview of subscription content, log in via an institution to check access.
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
Liao, X., Luo, Q., Zeng, Z.: Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing 71, 513–518 (2008)
Liao, X., Luo, Q., Zeng, Z., Guo, Y.: Global exponential stability in Lagrange sense for recurrent neural networks with time delays. Nonlinear Anal.: RWA 9, 1535–1557 (2008)
Luo, Q., Zeng, Z., Liao, X.: Global exponential stability in Lagrange sense for neutral type recurrent neural networks. Neurocomputing 74, 638–645 (2011)
Wu, A., Zeng, Z., Fu, C., Shen, W.: Global exponential stability in Lagrange sense for periodic neural networks with various activation functions. Neurocomputing 74, 831–837 (2011)
Wang, X., Jiang, M., Fang, S.: Stability analysis in Lagrange sense for a non-autonomous Cohen-Grossberg neural network with mixed delays. Nonlinear Anal.: TMA 70, 4294–4306 (2009)
Wang, B., Jian, J., Jiang, M.: Stability in Lagrange sense for Cohen-Grossberg neural networks with time-varying delays and finite distributed delays. Nonlinear Anal.: Hybrid Syst. 4, 65–78 (2010)
Tu, Z., Jian, J., Wang, K.: Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Nonlinear Anal.: RWA 12, 2174–2182 (2011)
Muralisankar, S., Gopalakrishnan, N., Balasubramaniam, P.: An LMI approach for global robust dissipativity analysis of T-S fuzzy neural networks with interval time-varying delays. Expert Syst. Appl. 39, 3345–3355 (2012)
Berman, A., Plemmons, R.: Nonnegative Matrices in Mathematical Sciences. Academic Press, New York (1979)
Gahinet, P., Nemirovski, A., Laub, A., Chilali, M.: LMI control toolbox user’s guide. Mathworks, Natick (1995)
Li, X.: Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Applied Mathematics and Computation 215, 292–307 (2009)
Liao, X., Fu, Y., Xie, S.: Globally exponential stability of Hopfied networks. Adv. Syst. Sci. Appl. 5, 533–545 (2005)
Halanay, A.: Differential Equations: Stability, Oscillations, Time Lags. Academic Press, New York (1966)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, X., Chen, X., Qi, H. (2013). Global Robust Exponential Stability in Lagrange Sense for Interval Delayed Neural Networks. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-39065-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39064-7
Online ISBN: 978-3-642-39065-4
eBook Packages: Computer ScienceComputer Science (R0)