A NOVEL GLOBAL EXPONENTIAL STABILITY RESULT FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH VARIABLE DELAYS

2006 ◽  
Vol 16 (06) ◽  
pp. 467-472 ◽  
Author(s):  
QIANG ZHANG ◽  
XIAOPENG WEI ◽  
JIN XU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Stability Condition ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Unique Equilibrium ◽  
Variable Delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.

EXPONENTIAL STABILITY ANALYSIS OF NEURAL NETWORKS WITH VARIABLE DELAYS

2010 ◽  
Vol 20 (05) ◽  
pp. 1541-1549 ◽  
Author(s):  
MAN-CHUN TAN ◽  
YAN ZHANG ◽  
WEN-LI SU ◽  
YU-NONG ZHANG
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Delays

Some sufficient conditions to ensure the existence, uniqueness and global exponential stability of the equilibrium point of cellular neural networks with variable delays are derived. These results extend and improve the existing ones in the literature. Two illustrative examples are given to demonstrate the effectiveness of our results.

scholarly journals Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

2009 ◽  
Vol 43 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Sannay Mohamad ◽  
Haydar Akça ◽  
Valéry Covachev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Continuous Time ◽  
Global Exponential Stability ◽  
Exponential Convergence ◽  
Unique Equilibrium ◽  
Transmission Delays

Abstract A discrete-time analogue is formulated for an impulsive Cohen- -Grossberg neural network with transmission delay in a manner in which the global exponential stability characterisitics of a unique equilibrium point of the network are preserved. The formulation is based on extending the existing semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the p-norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an M-matrix. The main result yields a Lyapunov exponent that involves the magnitude and frequency of the impulses. One can use the result for deriving the exponential stability of non-impulsive discrete-time neural networks, and also for simulating the exponential stability of impulsive and non-impulsive continuous-time networks.

scholarly journals On Global Exponential Stability of Discrete-Time Hopfield Neural Networks with Variable Delays

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Qiang Zhang ◽  
Xiaopeng Wei ◽  
Jin Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Hopfield Neural Networks ◽  
Difference Inequality ◽  
Variable Delays

Global exponential stability of a class of discrete-time Hopfield neural networks with variable delays is considered. By making use of a difference inequality, a new global exponential stability result is provided. The result only requires the delay to be bounded. For this reason, the result is milder than those presented in the earlier references. Furthermore, two examples are given to show the efficiency of our result.

scholarly journals Global Exponential Stability of Discrete-Time Multidirectional Associative Memory Neural Network with Variable Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wang ◽  
Tiejun Zhou ◽  
Xiaolan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Associative Memory ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Sufficient Condition ◽  
Variable Delays ◽  
Exponentially Stable ◽  
Inequality Technique

A discrete-time multidirectional associative memory neural networks model with varying time delays is formulated by employing the semidiscretization method. A sufficient condition for the existence of an equilibrium point is given. By calculating difference and using inequality technique, a sufficient condition for the global exponential stability of the equilibrium point is obtained. The results are helpful to design global exponentially stable multidirectional associative memory neural networks. An example is given to illustrate the effectiveness of the results.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

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