Robust Exponential Stability Analysis for Interval Neural Networks with Time Delay

2011 ◽  
Vol 58-60 ◽  
pp. 2597-2601
Author(s):  
Shou Yi Qian ◽  
Li Xie
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Exponential Stability ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Transformations ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Interval Neural Networks

The problem of robust exponential stability analysis for nonlinear uncertain interval neural networks with time delay is investigated. The nonlinear uncertainties are assumed to satisfy the cone constraint conditions. The interval parameters of the neural networks are equivalent to norm matched parameter uncertainties via some matrix transformations. The stable criteria for the uncertain interval neural networks with time delays are developed by use of the Lyapunov stability theory. All the stability conditions in this paper are presented in terms of linear matrix inequalities.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

scholarly journals Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hongwen Xu ◽  
Huaiqin Wu ◽  
Ning Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
State Estimation ◽  
Time Delays ◽  
Estimation Error ◽  
Linear Matrix ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Distributed Time Delays ◽  
Error System

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

scholarly journals Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yanke Du ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Global Robust Exponential Stability

A class of interval neural networks with time-varying delays and distributed delays is investigated. By employingH-matrix andM-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

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