scholarly journals Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
J. Thipcha ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Associative Memory ◽  
Global Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Bidirectional Associative Memory ◽  
Lower And Upper Bounds ◽  
Delay Dependent

The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

scholarly journals New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Wu Wen ◽  
Kaibo Shi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Time Varying ◽  
Stability Criteria ◽  
Decision Variables ◽  
Mathematical Techniques ◽  
Delay Dependent ◽  
The Relationship

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.

DELAY-DEPENDENT STABILITY CRITERION FOR BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH INTERVAL TIME-VARYING DELAYS

2009 ◽  
Vol 23 (01) ◽  
pp. 35-46 ◽  
Author(s):  
JU H. PARK ◽  
O. M. KWON
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Stability Criterion ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Bidirectional Associative Memory ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

scholarly journals Novel Global Exponential Stability Criterion for Recurrent Neural Networks with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wenguang Luo ◽  
Xiuling Wang ◽  
Yonghua Liu ◽  
Hongli Lan
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Stability Criterion ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

The problem of global exponential stability for recurrent neural networks with time-varying delay is investigated. By dividing the time delay interval [0,τ(t)] intoK+1dynamical subintervals, a new Lyapunov-Krasovskii functional is introduced; then, a novel linear-matrix-inequality (LMI-) based delay-dependent exponential stability criterion is derived, which is less conservative than some previous literatures (Zhang et al., 2005; He et al., 2006; and Wu et al., 2008). An illustrate example is finally provided to show the effectiveness and the advantage of the proposed result.

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