New delay-dependent global asymptotic stability condition for Hopfield neural networks with time-varying delays

2009 ◽  
Vol 6 (4) ◽  
pp. 415-419 ◽  
Author(s):  
Guang-Deng Zong ◽  
Jia Liu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Networks ◽  
Time Varying ◽  
Delay Dependent ◽  
Asymptotic Stability Condition

DELAY-DEPENDENT ASYMPTOTIC STABILITY OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 245-250 ◽  
Author(s):  
SHENGYUAN XU ◽  
JAMES LAM ◽  
DANIEL W. C. HO
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Unique Equilibrium ◽  
Delay Dependent ◽  
Asymptotic Stability Condition

This paper considers the problem of stability analysis for neural networks with time-varying delays. The time-varying delays under consideration are assumed to be bounded but not necessarily differentiable. In terms of a linear matrix inequality, a delay-dependent asymptotic stability condition is developed, which ensures the existence of a unique equilibrium point and its global asymptotic stability. The proposed stability condition is easy to check and less conservative. An example is provided to show the effectiveness of the proposed condition.

Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks with Time-Varying Delays

2010 ◽  
Vol 139-141 ◽  
pp. 1714-1717
Author(s):  
Wen Guang Luo ◽  
Yong Hua Liu ◽  
Hong Li Lan
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
The Stability ◽  
Delay Dependent

In this paper, the problem of global asymptotic stability in the mean square for stochastic fuzzy cellular neural networks (SFCNN) with time-varying delays is investigated. By constructing a newly proposed Lyapunov-Krasovskii function (LKF) and using Ito’s stochastic stability theory, a novel delay-dependent stability criterion is derived. The obtained stability result is helpful to design the stability of fuzzy cellular neural networks (FCNN) with time-varying delays when stochastic noise is taken into consideration. Since it is presented in terms of a linear matrix inequality (LMI), the sufficient condition is easy to be checked efficiently by utilizing some standard numerical packages such as the LMI Control Toolbox in Matlab. Finally, an illustrate example is given to verify the feasibility and usefulness of the proposed result.

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