DELAY-DEPENDENT GLOBAL ROBUST ASYMPTOTIC STABILITY ANALYSIS OF BAM NEURAL NETWORKS WITH TIME DELAY: AN LMI APPROACH

2007 ◽  
Vol 03 (01) ◽  
pp. 57-68 ◽  
Author(s):  
XU-YANG LOU ◽  
BAO-TONG CUI
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Lmi Approach ◽  
Global Robust Asymptotic Stability ◽  
Dependent Property ◽  
Delay Dependent ◽  
Robust Asymptotic Stability

The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays is studied. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

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.

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.

scholarly journals Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Yonggang Chen ◽  
Weiping Bi ◽  
Yuanyuan Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Bam Neural Networks ◽  
Delay Dependent ◽  
Slack Matrices

This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI). Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

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