Robust stability of stochastic fuzzy impulsive recurrent neural networks with\\ time-varying delays

Document Type: Research Paper

Author

Department of Mathematics, Thiruvalluvar University, Vellore - 632 106, Tamilnadu, India

Abstract

In this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varying
delays which are represented by the Takagi-Sugeno (T-S) fuzzy models is considered. A novel Linear Matrix Inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural networks with time-varying
delays. The results are related to the size of delay and impulses.
Finally, numerical examples and simulations are given to demonstrate the correctness of the theoretical results.

Keywords


bibitem{SA2} S. Arik, {it An analysis of exponential stability of
delayed neural networks with time varying delays},
 Neural Netw., textbf{17} (2004), 1027--1031.

bibitem{SA1} S. Arik, {it Novel results for global robust stability
of delayed neural networks},  Chaos Solitons Fractals, textbf{39} (2009), 1604--1614.

   bibitem{Be} R. Belohlavek, {it Fuzzy logical bidirectional
associative memory}, Information Sciences, textbf{128}
(2000),  91--103.

 bibitem{BF} S. A. Billings and C. F. Fung, {it Recurrent radial
basis function networks for adaptive noise cancellation},
Neural Netw., textbf{8} (1995), 273 -- 290.

 bibitem{BI} J. J. Blake, L. P. Maguire, T. M. McGinnity,
B. Roche and L. J. McDaid, {it The implementation of fuzzy systems,
neural networks and fuzzy neural networks using FPGAs},
Information Sciences, {bf 112} (1998),  151--168.

 bibitem{BGFB}  B. Boyd, L. Ghoui, E. Feron and V. Balakrishnan,
{it Linear Matrix Inequalities in System and Control Theory},
philadephia, PA, SIAM, 1994.

bibitem{CF}  Y. Y. Cao and P. M. Frank, {it Analysis and synthesis of
nonlinear time-delay system via fuzzy control approach},
IEEE Trans Fuzzy Syst., textbf{8} (2000), 200 –- 211.

bibitem{GNLC} P. Gahinet, A. Nemirovski, A. Laub and M. Chilali,
{it LMI control toolbox user's guide},  Massachusetts, The Mathworks,
1995.

 bibitem{GE} Y. Gao and M. J. Er, {it Modelling, control, and stability
analysis of non-linear systems using generalized fuzzy neural
networks}, Internat. J. Systems Science, textbf{34} (2003), 427 --
 438.

bibitem{GKW} C. L. Giles, G. M. Kuhn and R. J. Williams, {it Dynamic
recurrent neural networks: Theory and applications}, IEEE
Trans. Neural Netw., textbf{5} (1994),  153 -- 156.

  bibitem{ZHG} Z. H. Guan, J. Lam and G. Chen, {it On impulsive
autoassociative neural networks}, Neural Netw., textbf{13}
(2000), 63–69.

 bibitem{H} J. Hale and S. M. Verduyn Lunel, {it Introduction to
Functional Differential Equations}, New York, Springer, 1993.

 bibitem{MH} M. Han, Y. Sun and Y. Fan, {it An improved fuzzy neural
network based on T–S model},  Expert Syst. Appl.,
  textbf{34} (2008), 2905–-2920.

 bibitem{YYH} Y. Y. Hou, T. L. Liao and Y. Y. Yan, {it Stability
analysis of Takagi-Sugeno fuzzy cellular neural networks with time
varying delays}, IEEE Trans. Syst. Man Cybrn. Part B,
{bf 37} textbf{(3)} (2007), 720--726.

bibitem{HW} S. Hu and J. Wang, {it Global asymptotic stability and
global exponential stability of continuous time recurrent neural
networks}, IEEE Trans. Automat. Control,  textbf{47}
(2002), 802 -- 807.

 bibitem{HLM} S. Hu, X. Liao and X. Mao, {it Stochastic Hopfield
neural networks}, J. Phys. A: Math. Gen.,  textbf{9}
(2004), 47 -- 53.

 bibitem{HHL} H. Huang, D. Ho and J. Lam, {it Stochastic stability
analysis of fuzzy Hopfield neural networks with time-varying
delays}, IEEE Trans. Circ. Syst. II, Exp. Briefs,
textbf{52} (2005),  251 -- 255.

 bibitem{HC} H. Huang and J. Cao, {it Exponential stability analysis of
uncertain stochastic neural networks with multiple delays},
Nonlinear Anal: R W A, textbf{8} (2007),  646--653.

 bibitem{IJFS1} M.    Khasheri, M. Bijari and S. R. Hejazi, {it An extented fuzzy
  artificial neural networks model for time series forecasting},
 Iranain Journal of Fuzzy Systems, {bf 8} textbf{(3)}, (2011),  45--66.

 bibitem{L} V. Lakshmikantham, D. D. Bainov and P. S. Simeonov,
{it Theory of Impulsive Differential Equations}, Singapore, World
Scientific, 1989.

bibitem{VL} V. Lakshmikantham and X. Z. Liu, {it Impulsive hybrid systems and
stability theory}, International Journal of Nonlinear
Differential Equations, textbf{5}, (1999), 9–17.

bibitem{LC1} J. Liang and J. Cao, {it Boundedness and stability for
recurrent neural networks with variable coefficients and
time-varying delays}, Phys. Lett. A, textbf{318} (2003), 53
-– 64.

 bibitem{LM} X. Liao and X. Mao, {it Exponential stability and
instability of stochastic neural networks}, Stoch. Anal.
Appl., textbf{14} (1996), 165 –- 185.

bibitem{LZ} X. D, Liu and Q. L. Zhang, {it New approaches to H1
controller designs based on fuzzy observers for T–S fuzzy systems
via LMI}, Automatica, textbf{39} (2003), 1571 –- 1582.

 bibitem{BL} B. Liu and P. Shi, {it Delay-range-dependent stability for
fuzzy BAM neural networks with time-varying delays}, Phys.
Lett. A, textbf{373} (2009), 1830--1838.

  bibitem{IJFS2} J. Liu, Z. Gu, H. Han and  S. Hu, {it T- S fuzzy model - based memory control for discrete - time system
 with random input delay},  Iran. J. Fuzzy Syst., textbf{8(3)} (2011), 67-79.

bibitem{LC} X. Lou and B. Cui, {it Robust asymptotic stability of
uncertain fuzzy BAM neural networks with time-varying delays},
Fuzzy sets and systems,  textbf{158} (2007), 2746 -- 56.

bibitem{XM} X. Mao, N. Koroleva and A. Rodkina, {it Robust stability
of  uncertain stochastic delay differential equations},
Systems Control. lett., textbf{35} (1998), 325 -– 336.

 bibitem{MS1} M. Syed Ali and P. Balasubramaniam, {it Robust stability
of uncertian stochastic fuzzy BAM neural networks with time
varying delay}, Phys. Lett. A, textbf{372} (2008),
5159--5166.

 bibitem{MS2}  M. Syed Ali and  P. Balasubramaniam, {it Stability analysis of uncertain fuzzy Hopfield
neural networks with time delays}, Communic.
Nonlin.  Numeric. Simul., textbf{14} (2009), 2776--2783.

 bibitem{MS3} M. Syed Ali and  P. Balasubramaniam, {it Robust stability of uncertain fuzzy Cohen-Grossberg BAM
neural networks with time-varying delays}, Expert Syst.
Appl., textbf{36} (2009), 10583--10588.

bibitem{TS} T. Takagi and M. Sugeno,  {it Fuzzy identification of
systems and its applications to modeling and control}, IEEE
Trans. Syst. Man, Cybern., textbf{15} (1985), 116 -- 132.

 bibitem{TY1} T. Yang, {it Impulsive control}, IEEE Trans.
Automat. Control,  textbf{44}(5) (1999), 1081-1083.

 bibitem{TY2} T. Yang, {it Impulsive system and control:theory and
applications},  Huntington, NY, Nova Science Publishers, 2001.

bibitem{ZP} Y. Zhang and A. H. Pheng, {it Stability of fuzzy systems
with bounded uncertain delays}, IEEE Trans. Fuzzy Syst.,
textbf{10} (2002), 92 -– 97.

bibitem{Z1} H. Zhang, {it Robust exponential stability of recurrent
neural networks with multiple time varying delays}, IEEE
Trans. Circ. Syst. II, Exp. Briefs, textbf{54} (2007), 730 -- 734.

 bibitem{YZ1} Y. Zhang and J. T. Sun,{it Boundedness of the solutions
of impulsive differential systems with time-varying delay},
Appl. Math. Comput., textbf{154} (2004), 279–288.

 bibitem{YZ2} Y. Zhang and J. T. Sun, {it Stability of impulsive neural
networks with time delays}, Phys. Lett. A,  textbf{348}
(2005), 44–-50.

bibitem{QZ} Q. Zhang, X. Wei and J. Xu, {it Delay-dependent exponential
stability of cellular neural networks with time varying delays},
Chaos Solitons Fractals, textbf{23} (2005),  1363-1369.