Abstract
This paper deals with the global exponential stability in the mean square of fuzzy cellular neural networks with time-varying delays and Markovian jumping parameters. By constructing suitable Lyapunov functionals, we obtain several sufficient conditions which can be expressed in terms of linear matrix inequalities (LMIs). The proposed LMI results are computationally efficient as it can be solved numerically by using Matlab LMI toolbox. An example is given to show the effectiveness of the results.
Similar content being viewed by others
References
Yang T, Yang LB, Wu CW, Chua LO (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE international workshop on cellular neural networks and applications, pp 181–186
Yang T, Yang LB (1996) The global stability of fuzzy cellular neural networks. IEEE Trans Circuits Syst I 43:880–883
Wang LS, Xu DY (2003) Asymptotic behavior of a class of reaction-diffusion equations with delays. J Math Anal Appl 281:439–453
Wang LS, Gao YY (2006) Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays. Phys Lett A 350:342–348
Wang LS, Xu DY (2002) Global asymptotic stability of bidirection associative memory neural networks with S-type distributed delays. Int J Syst Sci 33:869–877
Yang T, Yang LB, Wu CW, Chua LO (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE international workshop on cellular neural networks and applications, pp 225–230
Wang ST, Korris FL, Chung K, Duan D (2007) Applying the improved fuzzy cellular neural network IFCNN to white blood cell detection. Neurocomputing 70:1348–1359
Barbounis TG, Theocharis JB (2007) A locally recurrent fuzzy neural network with application to the wind speed prediction using spatial correlation. Neurocomputing 70:1525–1542
Xu SY, Lam J, Ho DWC, Zou Y (2005) Delay-dependent exponential stability for a class of neural networks with time delays. J Comput Appl Math 183:16–28
Lou XY, Cui BT (2007) Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Sets Syst 158(24):2746–2756
Liang JL, Cao JD (2006) A based-on LMI stability criterion for delayed recurrent neural networks. Chaos Solitons Fractals 28:154–160
Krasovskii NM, Lidskii EA (1961) Analytical design of controllers in systems with random attributes. Autom Remote Control 22:1021–2025
Sworder D (1969) Feedback control of a class of linear systems with jump parameters. IEEE Trans Automat Control, 14(1):9–14
Ji Y, Chizeck HJ (1990) Controllability, stability and continuous-time Markovian jump linear quadratic control. IEEE Trans Automat Control 35:777–788
Feng X, Loparo KA, Ji Y, Chizeck HJ (1992) Stochastic stability properties of jump linear systems. IEEE Trans Automat Control 37:38–53
Chen WH, Guan ZH, Lu X (2004) Delay-dependent output feedback stabilization of Markovian jump system with time-delay. IEE Proc Control Theory Appl 151:561–566
Wang ZD, Liu YR, Yu L, Liu XH (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356:346–352
Lou XY, Cui BT (2007) Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J Math Anal Appl 328:316–326
Sanchez EN, Perez JP (1999) Input-to-state stability (ISS) analysis for dynamic NN. IEEE Trans Circuits Syst I 46:1395–1398
Acknowledgments
The authors would like to thank the Editor and the anonymous referees for their very valuable comments and helpful suggestions, which have been very useful for improving this work. This research is supported by the Youth Science Foundation of Shanxi Province (2010021001-2), the National Sciences Foundation of China (10901145), the Top Young Academic Leaders of Higher Learning Institutions of Shanxi, the National Natural Science Foundation of China (under Grant No. 60771026 and No. 10771199), the Programme for New Century Excellent Talents in University (NCET050271), and the Special Scientific Research Foundation for the Subjects of Doctors in University (20060110005).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Han, W., Liu, Y. & Wang, L. Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters. Neural Comput & Applic 21, 67–72 (2012). https://doi.org/10.1007/s00521-011-0685-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-011-0685-4