Abstract
This paper is devoted to global robust stability analysis of the general recurrent neural networks with time-varying parametric uncertainty and time-varying delays. To remove the dependence on the size of time-delays, Lyapunov-Razumikhin stability theorem and LMI approach are applied to derive the global robust stability conditions for the neural networks. Then delay-dependent global robust stability criteria are developed based on integrating Lyapunov-Krasovskii functional method and LMI approach. These stability criteria are in term of the solvability of linear matrix inequalities.
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References
Cao, Y.Y., Sun, Y.X., Cheng, C.: Delay-Dependent Robust Stabilization of Uncertain Systems with Multiple State Delays. IEEE Trans. Automatic Control 43, 1608–1612 (1998)
Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Applied Math. Scinces, vol. 99. Springer, New York (1993)
Niculescu, S.I.: Delay Effects on Stability: An Robust Control Approach. Lecuture Notes in Control and Information Sciences. Springer, London (2001)
Liao, X.F., Chen, G., Sanchez, E.N.: Delay-dependent Exponential Stability Analysis of Delayed Neural Networks: An LMI Approach. Neural Networks 15, 855–866 (2002)
Cao, J., Wang, J.: Global Asymptotic and Robust Stability of Recurrent Neural Networks with Time Delays. IEEE Trans. on Circuits and systems-I 52, 417–425 (2005)
Cao, J., Ho, D.W.C.: A General Framework for Global Asymptotic Stability Analysis of Delayed Neural Networks Based on LMI Approach. Chaos, Solitons and Fractals 24, 1317–1329 (2005)
Huang, H., Ho, D.W.C., Cao, J.: Analysis of Global Exponenital Stability and Periodic Solutions of Neural Networks with Time-varying Delays. Neual Networks 18, 161–170 (2005)
Singh, V.: Robust Stability of Celluar Neural Networks with Delay: linear matrix inequality approach. IEE Proc.-Control Theory Appl. 151, 125–129 (2004)
Zhang, H., Li, C., Liao, X.F.: A Note on the Robust Stability of Neural Networks with Time Delay. Chaos Solitons and Fractals 25, 357–360 (2005)
Li, C., Liao, X.F., Zhang, R., Prasad, A.: Global Robust Exponential Stability Analysis for Interval Neural Networks with Time-varying Delays. Chao, Solitons and Fractals 25, 751–757 (2005)
Chen, A., Cao, J., Huang, L.: Global Robust Stability of Interval Cellular Neural Networks with Time-varying Delays. Chaos, Solitons and Fractals 23, 787–799 (2005)
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© 2006 Springer-Verlag Berlin Heidelberg
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Xu, J., Pi, D., Cao, YY. (2006). Global Robust Stability of General Recurrent Neural Networks with Time-Varying Delays. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_27
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DOI: https://doi.org/10.1007/11759966_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
eBook Packages: Computer ScienceComputer Science (R0)