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 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.

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.

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 Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 62
Author(s):  
Charuwat Chantawat ◽  
Thongchai Botmart ◽  
Rattaporn Supama ◽  
Wajaree Weera ◽  
Sakda Noinang
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
Exponential Stability ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Robust Exponential Stability ◽  
Attenuation Level ◽  
Delay Dependent

This paper is concerned the problem of robust H∞ control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H∞ performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H∞ control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

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.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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