Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

Abstract This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.

[1]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[2]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[4]  Meiqin Liu,et al.  Global asymptotic stability analysis of discrete-time Cohen–Grossberg neural networks based on interval systems , 2008 .

[5]  Rajendran Samidurai,et al.  Global asymptotic stability of BAM neural networks with mixed delays and impulses , 2009, Appl. Math. Comput..

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

[7]  Ju H. Park,et al.  On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays , 2008, Appl. Math. Comput..

[8]  Jinde Cao,et al.  A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach , 2005 .

[9]  Baotong Cui,et al.  Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays , 2009 .

[10]  Ju H. Park.  Robust stability of bidirectional associative memory neural networks with time delays , 2006 .

[11]  Shengyuan Xu,et al.  Improved robust absolute stability criteria for uncertain time-delay systems , 2007 .

[12]  Xuyang Lou,et al.  On the global robust asymptotic stability of BAM neural networks with time-varying delays , 2006, Neurocomputing.

[13]  S. Arik.  Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays , 2006 .

[14]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

[15]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[16]  T. Liao,et al.  Globally exponential stability condition of a class of neural networks with time-varying delays , 2005 .

[17]  Shengyuan Xu,et al.  Delay-Dependent asymptotic Stability of Neural Networks with Time-Varying Delays , 2008, Int. J. Bifurc. Chaos.

[18]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[19]  Lisheng Wang,et al.  Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[21]  Jinde Cao,et al.  Stability and bifurcation of a class of discrete-time neural networks , 2007 .

[22]  Sabri Arik,et al.  Global stability of a class of neural networks with time-varying delay , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Jinde Cao,et al.  Existence and stability of almost periodic solution for BAM neural networks with delays , 2003, Appl. Math. Comput..

[24]  Ralph R. Martin,et al.  Discrete-time BAM neural networks with variable delays , 2007 .

[25]  Tianguang Chu,et al.  Exponential stability of neural networks with variable delays via LMI approach , 2006 .

[26]  Jinde Cao,et al.  Global asymptotic stability of delayed bi-directional associative memory neural networks , 2003, Appl. Math. Comput..

[27]  Min Wu,et al.  Global Exponential Stability of Discrete-Time BAM Neural Networks With Variable Delays , 2007, 2007 IEEE International Conference on Control and Automation.

[28]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .