New global asymptotic stability criteria of Hopfield neural network with time-varying delays

2008 ◽  
Author(s):  
Zhengxia Wang ◽  
Degang Yang ◽  
Fengqing Han ◽  
Xinyuan Liang
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Network ◽  
Time Varying ◽  
Stability Criteria

scholarly journals Delay-dependent asymptotic stability for neural networks with time-varying delays

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
Xiaofeng Liao ◽  
Xiaofan Yang ◽  
Wei Zhang
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Dynamical Behavior ◽  
Network Models ◽  
Time Varying ◽  
Stability Criteria ◽  
Neural Network Models ◽  
Neuron System ◽  
The Neural Network ◽  
Delay Dependent

We study the dynamical behavior of a class of neural network models with time-varying delays. By constructing suitable Lyapunov functionals, we obtain sufficient delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.

LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (03) ◽  
pp. 257-265 ◽  
Author(s):  
TAO LI ◽  
CHANGYIN SUN ◽  
XIANLIN ZHAO ◽  
CHONG LIN
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Activation Functions ◽  
Different Types ◽  
Conservative Result

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

scholarly journals A New Criterion for Exponential Stability of a Class of Hopfield Neural Network with Time-Varying Delay Based on Gronwall’s Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Faming Guo ◽  
Ricai Luo ◽  
Xiaolan Qin ◽  
Yunfei Yi
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Hopfield Neural Network ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Gronwall’S Inequality ◽  
Variation Of Constants ◽  
New Criterion ◽  
Varying Delay

In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays. Different from the existing results, we establish new stability criteria by employing the method of variation of constants and Gronwall’s integral inequality. Finally, we give several examples to show the effectiveness and applicability of the obtained criterion.

ON THE GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED NEURAL NETWORKS

2005 ◽  
Vol 15 (12) ◽  
pp. 4019-4025 ◽  
Author(s):  
ZHAOHUI YUAN ◽  
DEWEN HU ◽  
LIHONG HUANG ◽  
GUOHUA DONG
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Functional Method ◽  
Activation Functions ◽  
Delayed Neural Networks ◽  
System Parameters ◽  
Lyapunov Functional Method

In this paper, the problem of the global asymptotic stability (GAS) of a class of delayed neural network is investigated. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions, using some existing results for the existence and uniqueness of the equilibrium point, we obtain a couple of general results concerning GAS by means of Lyapunov functional method without the assumption of symmetry of interconnection matrix. Our results improve and extend some previous works of other researchers. Moreover, our conditions are presented in terms of system parameters, which have leading significance in designs and applications of GAS for Hopfield neural network (HNNs) and delayed cellular neural network (DCNNs).

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