Robust stability analysis of Takagi—Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

In this paper, the global stability of Takagi—Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.

[1]  X. Mao,et al.  Robust stability of uncertain stochastic differential delay equations , 1998 .

[2]  K. Gopalsamy,et al.  Exponential stability of artificial neural networks with distributed delays and large impulses , 2008 .

[3]  Pagavathigounder Balasubramaniam,et al.  Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays , 2008 .

[4]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[5]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[6]  Yong-Yan Cao,et al.  Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models , 2001, Fuzzy Sets Syst..

[7]  S. Arik.  An improved global stability result for delayed cellular neural networks , 2002 .

[8]  Kwok-Wo Wong,et al.  Global exponential stability for a class of generalized neural networks with distributed delays , 2004 .

[9]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[10]  Zidong Wang,et al.  An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays , 2008 .

[11]  Gang Feng,et al.  Analysis and design for a class of complex control systems Part I: Fuzzy modelling and identification , 1997, Autom..

[12]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Zhi-Hong Guan,et al.  Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach , 2005, Syst. Control. Lett..

[14]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[15]  Jinde Cao,et al.  Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays , 2003 .

[16]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

[17]  Min Han,et al.  An improved fuzzy neural network based on T-S model , 2008, Expert Syst. Appl..

[18]  Jun-Juh Yan,et al.  Stability Analysis of Takagi–Sugeno Fuzzy Cellular Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Wagner Caradori do Amaral,et al.  A novel approach based on recurrent neural networks applied to nonlinear systems optimization , 2007 .

[20]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[21]  Jinde Cao,et al.  Multistability of competitive neural networks with time-varying and distributed delays , 2009 .

[22]  N. W. Rees,et al.  Stability analysis and design for a class of continuous-time fuzzy control systems , 1996 .

[23]  Huaguang Zhang,et al.  Robust Exponential Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[25]  Wenwu Yu,et al.  Global robust stability of neural networks with time varying delays , 2007 .

[26]  Xuyang Lou,et al.  Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays , 2007, Fuzzy Sets Syst..

[27]  James Lam,et al.  Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[29]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[31]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[32]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[33]  Long-Yeu Chung,et al.  Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays , 2007 .