An Linear Matrix Inequality Approach to the Global Asymptotic Stability for DelayedCellular Neural Networks

2007 ◽  
Vol 4 (7) ◽  
pp. 1274-1277
Author(s):  
Qiang Zhang ◽  
Xiaopeng Wei ◽  
Guangzhao Cui
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix Inequality ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

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.

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