scholarly journals Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yanke Du ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Robust Exponential Stability ◽  
Global Robust Exponential Stability

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

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.

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.

Exponential Stability of Stochastic Reaction-Diffusion Neural Networks with Mixed Delays in Procurement of Maintenance Material

2011 ◽  
Vol 105-107 ◽  
pp. 2315-2320
Author(s):  
Xiao Chen
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Exponential Stability ◽  
Effective Means ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Mixed Delays ◽  
The Neural Network ◽  
Discrete Time Delay

In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

Global Robust Exponential Stability of Cohen-Grossberg Neural Network with Time Varying Delays

2012 ◽  
Vol 182-183 ◽  
pp. 1135-1140 ◽  
Author(s):  
Rui Zhang ◽  
Chang Tao Wang
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Functional Method ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Inequality Technique ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for Cohen-Grossgerg neural network with parameter uncertainties and time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The proposed result is less restrictive, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

Global Robust Exponential Stability of Interval Cohen-Grossberg Neural Network with Time Varying Delays

2013 ◽  
Vol 756-759 ◽  
pp. 3884-3888 ◽  
Author(s):  
Rui Zhang ◽  
Jian Liu ◽  
Meng Xin Li ◽  
Mei Ju Liu
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Functional Method ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Inequality Technique ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for interval Cohen-Grossgerg neural network with time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The obtained stability criterion is dependent on the upper bound of time varying delays. The proposed result is less restrictive, and suitable of the cases of slow or fast time varying delays, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

Global Robust Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays

2012 ◽  
Vol 546-547 ◽  
pp. 772-777 ◽  
Author(s):  
Rui Zhang ◽  
Jian Liu ◽  
Ying Zhang ◽  
Chang Tao Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Robust Exponential Stability ◽  
Discrete Lyapunov Functional ◽  
Inequality Techniques ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium point is obtained for this system. The proposed result is less restrictive, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.

scholarly journals Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Quan Xu ◽  
Jibin Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Complex Valued

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

GLOBAL EXPONENTIAL STABILITY OF IMPULSIVE FUZZY CELLULAR NEURAL NETWORKS WITH DELAYS AND DIFFUSION

2009 ◽  
Vol 19 (01) ◽  
pp. 245-261 ◽  
Author(s):  
KELIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Mixed Delays ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique ◽  
And Diffusion

In this paper, a class of impulsive fuzzy cellular neural networks (FCNNs) with mixed delays and diffusion is formulated and investigated. By establishing an intergro-differential inequality, applying M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of an equilibrium point for impulsive FCNNs with mixed delays and diffusion. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulses. These results generalize and improve the earlier publications. Some examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of FCNNs.

scholarly journals An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chuangxia Huang ◽  
Hanfeng Kuang ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Average Dwell Time Method ◽  
Uniformly Ultimate Boundedness

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

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