Abstract
Cellular neural networks (CNNs) introduced by Chua and Yang in 1988 are recurrent artificial neural networks. Due to their cyclic connections and to the neurons’ nonlinear activation functions, recurrent neural networks are nonlinear dynamic systems, which display stable and unstable fixed points, limit cycles and chaotic behavior. Since the field of neural networks is still a recent one, improving the stability conditions for such systems is an obvious and quasi-permanent task. This paper focuses on CNNs affected by time delays. We are interested to obtain sufficient conditions for the asymptotic stability of a cellular neural network with time delay feedback and zero control templates. Due to their sector restricted nonlinearities, stability of the neural networks is strongly connected to robust stability. With respect to this we shall use a quadratic Liapunov functional constructed via the technique due to V. L. Kharitonov for uncertain linear time delay systems, combined with an approach suggested by Malkin for systems with sector restricted nonlinearities.
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References
Barbashin, E.A.: Liapunov functions (in Russian), 58–60. Nauka Publ. House, Moscow (1970)
Chua, L., Yang, L.: Cellular neural networks: theory and applications. IEEE Trans. Circuits and Systems CAS-35, 1257–1290 (1988)
Danciu, D.: Stability analysis of cellular neural networks with time delays. In: Int. Symp. Syst. Th., Rob., Comp. & Proc. Inf. - SINTES 11, Craiova, Romania, pp. 32–34 (2003)
Danciu, D.: A method for time delay cellular neural networks stability analysis. In: Int. Carpathian Contr. Conf. 2004 - ICCC 2004, Zakopane, Poland, pp. 65–70 (2004)
Danciu, D., Răsvan, V.: Stability Criteria for Cellular Neural Networks. Annals ”Dunărea de Jos” University of Galaţi, Series: Electrotechnics, Electronics, Automatic Control, Informatics 3 (2000)
Gu, K., Kharitonov, V.L., Chen, J.: Stability and robust stability of time delay systems. Birkhäuser, Boston (2003)
Halanay, A.: Differential Equations. Stability. Oscillations. Time Lags (in Romanian). Editura Academiei, Bucharest (1963)(English improved version by Academic Press, Mathematics in Science and Engineering Series 23 (1966)
Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, Heidelberg (1993)
Kharitonov, V.L., Zhabko, A.P.: Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica 39, 15–20 (2003)
Malkin, I.G.: Stability of Motion (in Russian). Gostekhizdat, Moscow (1952)
Popov, V.M.: Hyperstability of Control Systems (in Romanian) Editura Academiei, Bucharest (1966) (English improved version by Springer Verlag (1973)
Răsvan, V.: Absolute Stability of Time Lag Control Systems (in Romanian). Editura Academiei, Bucharest (1975) (Russian improved version by Nauka Publ. House, Moscow (1983)
Yoshizawa, T.: Stability theory by Liapunov’s second method. Math. Soc. Japan, Tokyo (1966)
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Danciu, D., Răsvan, V. (2005). Stability Results for Cellular Neural Networks with Time Delays. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_45
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DOI: https://doi.org/10.1007/11494669_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26208-4
Online ISBN: 978-3-540-32106-4
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