Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach

Abstract This paper is interested in the problem of asymptotic stability analysis of Bidirectional Associative Memory (BAM) neural networks with time-varying delays via delta operator approach. The delays are assumed to exist in the nonlinear synaptic connection between different neural fields. Based on the Lyapunov–Krasovskii functional in delta domain, a new delay-dependent criterion for analyzing the asymptotic stability of BAM neural networks is obtained. Some previous results of continuous and discrete BAM systems are unified into the delta operator system framework due to the favorable numerical properties and the quasi-continuous performance of delta operator approach at high sampling rates. Since the sampling period is an explicit parameter in the results, it can be regulated to analyze the stability of systems. Numerical examples are presented to demonstrate the effectiveness of the developed theoretical results.

[1]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[2]  Huijun Gao,et al.  New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays , 2010, Neurocomputing.

[3]  Daniel W. C. Ho,et al.  Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case , 2010, IEEE Transactions on Signal Processing.

[4]  E. Jury,et al.  On Robust Stability of Discrete-Time Systems using Delta-Operators , 1992, 1992 American Control Conference.

[5]  Hao Liu,et al.  New stability criteria for BAM neural networks with time-varying delays , 2009, Neurocomputing.

[6]  Zidong Wang,et al.  Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon , 2011, IEEE Transactions on Neural Networks.

[7]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[8]  Guang-Hong Yang,et al.  Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay , 2008, 2008 American Control Conference.

[9]  Yonggang Chen,et al.  Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays , 2008 .

[10]  Zhang Duan-jin.  Robust stability analysis and control for fuzzy systems with uncertainties using the delta operator , 2003 .

[11]  W. Ebert.  Optimal filtered predictive control – a delta operator approach , 2001 .

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

[13]  C. Soh.  Robust discrete time systems using delta operators , 1991 .

[14]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[15]  Piotr Suchomski.  Numerically robust delta-domain solutions to discrete-time Lyapunov equations , 2002, Syst. Control. Lett..

[16]  Zidong Wang,et al.  Variance-Constrained Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements : The Finite-Horizon Case , 2010 .

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

[18]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[19]  Graham C. Goodwin,et al.  Rapprochement between continuous and discrete model reference adaptive control , 1986, Autom..

[20]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[21]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[22]  Zidong Wang,et al.  Sampled‐data H∞ filtering for stochastic genetic regulatory networks , 2011 .

[23]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[24]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[25]  Jinde Cao,et al.  LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks , 2005 .

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

[27]  Huijun Gao,et al.  ℋ∞ Fuzzy Control for Systems with Repeated Scalar Nonlinearities , 2009 .

[28]  J. Qiu,et al.  Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators , 2008 .

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

[30]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[31]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[32]  Wei Xing Zheng,et al.  Exponential Stability Analysis for Delayed Neural Networks With Switching Parameters: Average Dwell Time Approach , 2010, IEEE Transactions on Neural Networks.

[33]  Bing Chen,et al.  Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays , 2009, Neurocomputing.