Abstract
Global asymptotic stability problem for a general class of higher order recurrent neural networks (HRNN) with multiple delays has been studied based on delay-matrix decomposition method and linear matrix inequality (LMI) technique. The proposed stability criterion is suitable for a general class of multiple delayed higher order recurrent Neural Networks. Especially, for this system, we have also established corresponding LMI-based stability criteria which are simple in expression form and easy to check to deal with the different multiple delays. Compared with the existing results, our results are new and can be regarded as an alternative of M-matrix based stability results in the literature.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Zeng, Z., Wang, J., Liao, X.: Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications 50, 1353–1358 (2003)
Zhang, H., Wang, Z.: Global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Networks 18, 947–950 (2007)
Zhang, H., Wang, Z., Liu, D.: Global asymptotic stability of recurrent neural networks with multiple time varying delays. IEEE Trans. Neural Networks 19, 855–873 (2008)
Zhang, H., Wang, Z., Liu, D.: Robust stability analysis for interval cohen-grossberg neural network with unknown time-varying delays. IEEE Trans. Neural Networks 19, 1942–1955 (2008)
Ziegaus, C., Lang, E.: A neural implementation ofthe JADE algorithm (nJADE) using higher-order neurons. Neurocomputing 56, 79–100 (2004)
Xu, B., Liu, X., Liao, X.: Stability analysis of high-order Hopfield type neural networks with uncertainty. Neurocomputing 71, 508–512 (2008)
Xu, B., Wang, Q., Liao, X.: Global exponential stability of high order Hopfield type neural networks. Appl. Math. Comput. 174, 98–116 (2006)
Qiu, J.: Dynamics of high-order Hopfield neural networks with time delays. Neurocomputing 73, 820–826 (2010)
Cao, J., Liang, J., Lam, J.: Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199, 425–436 (2004)
Huo, H., Li, W., Tang, S.: Dynamics of high-order BAM neural networks with and without impulses. Applied Mathematics and Computation 215, 2120–2133 (2009)
Hu, H., Jiang, H., Teng, Z.: The boundedness of high-order Hopfield neural networks with variable delays. Neurocomputing 73, 2589–2596 (2010)
Ou, C.: Anti-periodic solutions for high-order Hopfield neural networks. Computers and Mathematics with Applications 56, 1838–1844 (2008)
Chen, T., Lu, W.: Stability analysis of dynamical neural networks. In: IEEE Int. Conf. Neural Networks and Signal Processing, Nanjing, China, December 14-17 (2003)
Chen, T.: Universal Approach to Study Delayed Dynamical Systems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005, Part I. LNCS, vol. 3610, pp. 245–253. Springer, Heidelberg (2005)
Liu, P., Yi, F., Guo, Q., Yang, J., Wu, W.: Analysison global exponential robust stability of reactioncdiffusion neural networks with s-type distributed delays. Physica D 237, 475–485 (2008)
Wang, L., Xu, D.: Global asymptotic stability of bidirectional associative memory neural networks with s-type distributed delays. Internat. J. Syst. Sci. 33, 869–877 (2002)
Wang, Z., Zhang, H., Liu, D., Feng, J.: LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays. In: Yu, W., He, H., Zhang, N. (eds.) ISNN 2009, Part I. LNCS, vol. 5551, pp. 463–471. Springer, Heidelberg (2009)
Chen, T.: Universal Approach to Study Delayed Dynamical Systems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005, Part I. LNCS, vol. 3610, pp. 245–253. Springer, Heidelberg (2005)
Chen, T.: Universal approach to study delayed dynamical systems. SCI, vol. 35, pp. 85–110 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Z., Zhao, Y., Lun, S. (2012). Global Stability of a Class of High-Order Recurrent Neural Networks with Multiple Delays. In: Zhang, H., Hussain, A., Liu, D., Wang, Z. (eds) Advances in Brain Inspired Cognitive Systems. BICS 2012. Lecture Notes in Computer Science(), vol 7366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31561-9_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-31561-9_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31560-2
Online ISBN: 978-3-642-31561-9
eBook Packages: Computer ScienceComputer Science (R0)