Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays

doi:10.1088/1674-1056/21/7/070207

摘要/Abstract

摘要： This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi--Sugeno (T--S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.

关键词: neutral neural networks, linear matrix inequality, Lyapunov stability, time varying delays

Abstract: This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi--Sugeno (T--S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.

Key words: neutral neural networks, linear matrix inequality, Lyapunov stability, time varying delays

中图分类号: (Delay and functional equations)

02.30.Ks

02.30.Sa (Functional analysis) 02.60.Cb (Numerical simulation; solution of equations) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

M. Syed Ali. Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays[J]. 中国物理B, 2012, 21(7): 70207-070207.

M. Syed Ali . Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays[J]. Chin. Phys. B, 2012, 21(7): 70207-070207.

参考文献 43

[1]	Cohen M and Grossberg S 1983 IEEE Trans. Syst. Man Cyber. 13 815.
[2]	Wang L and Zou X 2002 Neural Networks 15 415
[3]	Wang L and Zou X 2002 Physica D 170 162
[4]	Huang Z, Wang X and Xia Y 2008 Int. J. Circ. Theor. App. 36 345
[5]	Gau R S, Hsieh J G and Lien C H 2008 Int. J. Circ. Theor. App. 36 451
[6]	Zhang J 2004 Int. J. Circ. Theor. App. 32 11
[7]	Mohamad S 2003 Appl. Math. Comput. 135 17
[8]	Chua L O and Yang L 1988 IEEE Trans. Circ. Syst. I 35 1257
[9]	Yu W, Cao J and Wang J 2007 Neural Networks 20 810
[10]	Baldi P and Atiya A F 1994 IEEE Trans. Neural Netw. 5 612
[11]	Liao X, Chen G and Sanchez E N 2002 Neural Networks 15 855
[12]	Wang Z, Lam J and Burnham K J 2002 IEEE Trans. Automat. Control 47 478
[13]	Du B and Lam J 2009 Neural Networks 22 343
[14]	Arik S 2000 IEEE Trans. Circ. Syst. I 47 1089
[15]	Arik S and Tavsanoglu V 2000 IEEE Trans. Circ. Syst. I 47 571
[16]	Liao X, Wong K W, Wu Z and Chen G 2001 IEEE Trans. Circ. Syst. I 48 1355
[17]	Shi P and Shue S P 1999 IEEE Trans. Autom. Control 44 108
[18]	Singh V 2005 IEEE Trans. Circ. Syst. II 52 33
[19]	Arik S 2005 Chaos Soliton. Fract. 26 1407
[20]	Cao J and Huang D S and Qu Y 2005 Chaos Soliton. Fract. 23 221
[21]	Xu S, Lam J and Ho D W C 2005 Phys. Lett. A 342 322
[22]	Zuo Z and Wang Y 2006 Leucture Notes in Computer Science 4113 216
[23]	Park J H, Kwon O M and Lee S M 2008 J. Comput. Appl. Math. 196 224
[24]	Xu S, Lam J, Ho D W C and Zou Y 2005 J. Comput. Appl. Math. 183 16
[25]	Rakkiyappan R and Balasubramaniam P 2008 Neurocomputing 71 1039
[26]	Feng J, Xu S and Zou Y 2009 Neurocomputing 72 2576
[27]	Zhu J, Zhang Q and Yang C 2009 Neurocomputing 72 2609
[28]	Park J H and Kwon O M 2009 Chaos Soliton. Fract. 41 1174
[29]	Takagi T and Sugeno M 1985 IEEE Trans. Syst. Man. Cybern. 15 116
[30]	Takagi T and Sugeno M 1993 Fuzzy Sets and Systems 45 135
[31]	Cao Y Y and Frank P M 2001 Fuzzy Sets and Systems 124 213
[32]	Tanaka K, Ikede T and Wang H O 1996 IEEE Trans. Fuzzy Systems 4 1
[33]	Tanaka K, Ikede T and Wang H O 1997 Proc. IEEE Onternational Conference on Fuzzy Systems, July 5, 1997 Barcelona, Spain, p. 171
[34]	Tanaka K, Ikede T and Wang H O 1998 IEEE Trans. Fuzzy Systems 6 250
[35]	Huang H, Ho D W C and Lam J 2005 IEEE Trans. Circ. Syst. II 52 251
[36]	Lou X and Cui B 2007 Fuzzy Sets and Systems 158 2746
[37]	Syed Ali M and Balasubramaniam P 2009 Communications in Nonlinear Science and Numerical Simulation 14 2776
[38]	Syed Ali M and Balasubramaniam P 2009 Neurocomputing 72 1347
[39]	Liu B and Shi P 2009 Phys. Lett. A 373 1830
[40]	Li H, Chen B, Lin C and Zhou Q 2009 Neurocomputing 72 2017
[41]	Gahinet P, Nemirovski A, Laub A and Chilali M 1995 LMI Control Toolbox User's Guide (Massachusetts: The Mathworks)
[42]	Boyd B, Ghoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadephia: SIAM)
[43]	Mao X, Koroleva N and Rodkina A 1998 Systems Control. Lett. 35 325