Global Asymptotic Stability for Complex-Valued Neural Networks with Time-Varying Delays via New Lyapunov Functionals and Complex-Valued Inequalities

2017 ◽  
Vol 48 (2) ◽  
pp. 995-1017 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Dangli Hao
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Complex Valued

NOVEL STABILITY CONDITIONS FOR CELLULAR NEURAL NETWORKS WITH TIME DELAY

2001 ◽  
Vol 11 (07) ◽  
pp. 1853-1864 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
JUEBANG YU
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Research Work ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Time Varying Delay

In this paper, the global asymptotic stability of cellular neural networks with time delay is discussed using some novel Lyapunov functionals. Novel sufficient conditions for this type of stability are derived. They are less restrictive and more practical than those currently used. As a result, the design of cellular neural networks with time delay is refined. Our work can also be generalized to cellular neural networks with time-varying delay, a topic on which little research work has been done. By means of several different Lyapunov functionals, some sufficient conditions related to the global asymptotic stability for cellular neural networks with perturbations of time-varying delays are derived.

scholarly journals New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Global Asymptotic Stability ◽  
Positive Definite ◽  
Time Varying ◽  
Numerical Example ◽  
Definite Form ◽  
Takagi Sugeno

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods.

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