Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays

This paper is concerned with global asymptotic stability for a class of generalized neural networks (NNs) with interval time-varying delays, which include two classes of fundamental NNs, i.e., static neural networks (SNNs) and local field neural networks (LFNNs), as their special cases. Some novel delay-independent and delay-dependent stability criteria are derived. These stability criteria are applicable not only to SNNs but also to LFNNs. It is theoretically proven that these stability criteria are more effective than some existing ones either for SNNs or for LFNNs, which is confirmed by some numerical examples.

[1]  Xun-lin Zhu,et al.  Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays , 2009 .

[2]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Guang-Hong Yang,et al.  New Delay-Dependent Stability Results for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[4]  Qing-Long Han,et al.  Absolute stability of time-delay systems with sector-bounded nonlinearity , 2005, Autom..

[5]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Jun Wang,et al.  Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights , 2001, IEEE Trans. Autom. Control..

[7]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

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

[9]  Jun Wang,et al.  Global stability of a class of continuous-time recurrent neural networks , 2002 .

[10]  Qing-Long Han,et al.  New results for delay-dependent stability of linear systems with time-varying delay , 2002, Int. J. Syst. Sci..

[11]  Zhiqiang Zuo,et al.  Robust stability criterion for delayed cellular neural networks with norm-bounded uncertainties , 2007 .

[12]  Hong Qiao,et al.  A comparative study of two modeling approaches in neural networks , 2004, Neural Networks.

[13]  Min Wu,et al.  An improved global asymptotic stability criterion for delayed cellular neural networks , 2006, IEEE Transactions on Neural Networks.

[14]  Jyh-Ching Juang,et al.  Stability analysis of Hopfield-type neural networks , 1999, IEEE Trans. Neural Networks.

[15]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[16]  Xiaofeng Liao,et al.  Robust stability for interval Hopfield neural networks with time delay , 1998, IEEE Trans. Neural Networks.

[17]  Huaguang Zhang,et al.  An Augmented LKF Approach Involving Derivative Information of Both State and Delay , 2010, IEEE Transactions on Neural Networks.

[18]  Yijing Wang,et al.  A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[19]  Shu-Cherng Fang,et al.  Neurocomputing with time delay analysis for solving convex quadratic programming problems , 2000, IEEE Trans. Neural Networks Learn. Syst..

[20]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

[21]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[22]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[23]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[24]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[25]  Xuesong Jin,et al.  Global stability analysis in delayed Hopfield neural network models , 2000, Neural Networks.

[26]  Wen Yu,et al.  Stability Analysis of Nonlinear System Identification via Delayed Neural Networks , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[28]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[29]  Stanislaw H. Zak,et al.  On the Brain-State-in-a-Convex-Domain Neural Models , 1996, Neural Networks.

[30]  Hanyong Shao,et al.  Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[31]  Anthony N. Michel,et al.  Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory , 1990 .

[32]  Tao Li,et al.  Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[33]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[34]  Hong Qiao,et al.  A reference model approach to stability analysis of neural networks , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[35]  Huaguang Zhang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks With Time-Varying Delays , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

[36]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[37]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[38]  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.

[39]  DeLiang Wang,et al.  Emergent synchrony in locally coupled neural oscillators , 1995, IEEE Trans. Neural Networks.