Global Robust Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays

2012 ◽  
Vol 546-547 ◽  
pp. 772-777 ◽  
Author(s):  
Rui Zhang ◽  
Jian Liu ◽  
Ying Zhang ◽  
Chang Tao Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Robust Exponential Stability ◽  
Discrete Lyapunov Functional ◽  
Inequality Techniques ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium point is obtained for this system. The proposed result is less restrictive, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.

scholarly journals Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Yonggang Chen ◽  
Weiping Bi ◽  
Yuanyuan Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Bam Neural Networks ◽  
Delay Dependent ◽  
Slack Matrices

This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI). Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

2014 ◽  
Vol 989-994 ◽  
pp. 1877-1882 ◽  
Author(s):  
Liang Dong Guo ◽  
Jin Nie ◽  
You Shan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Bam Neural Networks ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Globally Exponential Stability ◽  
Delay Dependent

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

NOVEL STABILITY CRITERIA ON DISCRETE-TIME NEURAL NETWORKS WITH BOTH TIME-VARYING AND DISTRIBUTED DELAYS

2009 ◽  
Vol 19 (04) ◽  
pp. 269-283 ◽  
Author(s):  
TAO LI ◽  
AIGUO SONG ◽  
SHUMIN FEI
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Combination Methods

This paper investigates robust exponential stability for discrete-time recurrent neural networks with both time-varying delay (0 ≤ τm ≤ τ(k) ≤ τM) and distributed one. Through partitioning delay intervals [0,τm] and [τm,τM], respectively, and choosing an augmented Lyapunov-Krasovskii functional, the delay-dependent sufficient conditions are obtained by using free-weighting matrix and convex combination methods. These criteria are presented in terms of linear matrix inequalities (LMIs) and their feasibility can be easily checked by resorting to LMI in Matlab Toolbox in Ref. 1. The activation functions are not required to be differentiable or strictly monotonic, which generalizes those earlier forms. As an extension, we further consider the robust stability of discrete-time delayed Cohen-Grossberg neural networks. Finally, the effectiveness of the proposed results is further illustrated by three numerical examples in comparison with the reported ones.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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