Delay-Dependent Globally Exponential Stability Criteria for Static Neural Networks: An LMI Approach

2009 ◽  
Vol 56 (7) ◽  
pp. 605-609 ◽  
Author(s):  
Cheng-De Zheng ◽  
Huaguang Zhang ◽  
Zhanshan Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Stability Criteria ◽  
Lmi Approach ◽  
Globally Exponential Stability ◽  
Static Neural Networks ◽  
Delay Dependent

scholarly journals New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Wu Wen ◽  
Kaibo Shi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Time Varying ◽  
Stability Criteria ◽  
Decision Variables ◽  
Mathematical Techniques ◽  
Delay Dependent ◽  
The Relationship

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.

CONVERGENCE OF DISCRETE-TIME RECURRENT NEURAL NETWORKS WITH VARIABLE DELAY

2005 ◽  
Vol 15 (02) ◽  
pp. 581-595 ◽  
Author(s):  
JINLING LIANG ◽  
JINDE CAO ◽  
JAMES LAM
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Matrix Decomposition ◽  
Linear Matrix ◽  
Variable Delay ◽  
Stability Criteria ◽  
Lmi Approach ◽  
The Neural Networks

In this paper, some global exponential stability criteria for the equilibrium point of discrete-time recurrent neural networks with variable delay are presented by using the linear matrix inequality (LMI) approach. The neural networks considered are assumed to have asymmetric weighting matrices throughout this paper. On the other hand, by applying matrix decomposition, the model is embedded into a cooperative one, the latter possesses important order-preserving properties which are basic to our analysis. A sufficient condition is obtained ensuring the componentwise exponential stability of the system with specific performances such as decay rate and trajectory bounds.

scholarly journals Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

2013 ◽  
Vol 23 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Yang Liu ◽  
Rongjiang Yang ◽  
Jianquan Lu ◽  
Bo Wu ◽  
Xiushan Cai
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
High Order ◽  
Impulsive Effect ◽  
Time Varying ◽  
Stability Criteria ◽  
Globally Exponential Stability ◽  
Impulsive Differential Inequality

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

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