Abstract
In this paper, a class of complex-valued neural networks including two additive time-varying delay components has been discussed. By making use of the combinational Lyapunov-Krasovskii functional and free weighting matrix method, as well as matrix inequality technique, a delay-dependent criterion of stability is derived.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chen, T.: Global exponential stability of delayed Hopfield neural networks. Neural Netw. 14, 977–980 (2001)
Arik, S., Orman, Z.: Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Phys. Lett. A 341, 410–421 (2005)
Song, Q., Cao, J.: Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. 37, 733–741 (2007)
Kwon, O.M., Park, J.H.: New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays. Appl. Math. Comput. 205, 417–427 (2008)
Weera, W., Niamsup, P.: Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays. Neurocomputing 173, 886–898 (2016)
Zhao, Y., Gao, H., Mou, S.: Asymptotic stability analysis of neural networks with successive time delay components. Neurocomputing 71, 2848–2856 (2008)
Shao, H., Han, Q.: New delay-dependent stability criteria for neural networks with two additive time-varying delay components. IEEE Trans. Neural Netw. 22, 812–818 (2011)
Xiao, N., Jia, Y.: New approaches on stability criteria for neural networks with two additive time-varying delay components. Neurocomputing 118, 150–156 (2013)
Liu, Y., Lee, S.M., Lee, H.G.: Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components. Neurocomputing 151, 770–775 (2015)
Hirose, A.: Dynamics of fully complex-valued neural networks. Electron. Lett. 28, 1492–1494 (1992)
Lee, D.: Relaxation of the stability condition of the complex-valued neural networks. IEEE Trans. Neural Netw. 12, 1260–1262 (2001)
Hu, J., Wang, J.: Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans. Neural Netw. Learn. Syst. 23, 853–865 (2012)
Zhou, B., Song, Q.: Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 24, 1227–1238 (2013)
Chen, X., Song, Q.: Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing 121, 254–264 (2013)
Zhang, Z., Lin, C., Chen, B.: Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 1704–1708 (2014)
Liu, X., Chen, T.: Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans. Neural Netw. Learn. Syst. 27, 593–606 (2016)
Bohner, M., Sree Hari Rao, V., Sanyal, S.: Global stability of complex-valued neural networks on time scales. Differ. Equ. Dyn. Syst. 19, 3–11 (2011)
Fang, T., Sun, J.: Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans. Neural Netw. Learn. Syst. 25, 1709–1713 (2014)
Song, Q., Zhao, Z., Liu, Y.: Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168, 1044–1050 (2015)
Song, Q., Yan, H., Zhao, Z., Liu, Y.: Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects. Neural Netw. 79, 108–116 (2016)
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants 61473332, 11402214, and 61673169 and the Program of Chongqing Innovation Team Project in University under Grant CXTDX201601022.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Zhao, Z., Song, Q., Zhao, Y. (2017). Stability of Complex-Valued Neural Networks with Two Additive Time-Varying Delay Components. In: Cong, F., Leung, A., Wei, Q. (eds) Advances in Neural Networks - ISNN 2017. ISNN 2017. Lecture Notes in Computer Science(), vol 10261. Springer, Cham. https://doi.org/10.1007/978-3-319-59072-1_66
Download citation
DOI: https://doi.org/10.1007/978-3-319-59072-1_66
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59071-4
Online ISBN: 978-3-319-59072-1
eBook Packages: Computer ScienceComputer Science (R0)