scholarly journals Delay-Dependent Dynamics of Switched Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Wang ◽  
Haijun Hu ◽  
Zheng Jun ◽  
Yanxiang Tan ◽  
Li Liu
Keyword(s):  
Neural Networks ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Lyapunov Functional Method ◽  
Uniformly Ultimate Boundedness ◽  
Delay Dependent

This paper aims at studying the problem of the dynamics of switched Cohen-Grossberg neural networks with mixed delays by using Lyapunov functional method, average dwell time (ADT) method, and linear matrix inequalities (LMIs) technique. Some conditions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of the switched Cohen-Grossberg neural networks are developed. Our results extend and complement some earlier publications.

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.

scholarly journals Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Chuangxia Huang ◽  
Jie Cao ◽  
Peng Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Ultimate Boundedness ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Uniformly Ultimate Boundedness

We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN) with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI), and the average dwell time approach (ADT), some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.

scholarly journals Almost Sure Asymptotical Adaptive Synchronization for Neutral-Type Neural Networks with Stochastic Perturbation and Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Wuneng Zhou ◽  
Xueqing Yang ◽  
Jun Yang ◽  
Anding Dai ◽  
Huashan Liu
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Stochastic Perturbation ◽  
Adaptive Controller ◽  
Functional Method ◽  
Markovian Switching ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Lyapunov Functional Method ◽  
New Criterion

The problem of almost sure (a.s.) asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching is researched. Firstly, we proposed a new criterion of a.s. asymptotic stability for a general neutral-type stochastic differential equation which extends the existing results. Secondly, based upon this stability criterion, by making use of Lyapunov functional method and designing an adaptive controller, we obtained a condition of a.s. asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching. The synchronization condition is expressed as linear matrix inequality which can be easily solved by Matlab. Finally, we introduced a numerical example to illustrate the effectiveness of the method and result obtained in this paper.

scholarly journals Stability of delay neural networks with uncertainties via delayed intermittent control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yujuan Tian ◽  
Fei Wang ◽  
Yao Wang ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Weighting Matrix ◽  
Control Scheme ◽  
Globally Asymptotical Stability ◽  
The Stability ◽  
Delay Dependent

Abstract In this paper, we investigate the stability of neural networks with both time-varying delays and uncertainties. A novel delayed intermittent control scheme is designed to ensure the globally asymptotical stability of the addressed system. Some new delay dependent sufficient criteria for globally asymptotical stability results are derived in term of linear matrix inequalities (LMIs) by using free-weighting matrix techniques and Lyapunov–Krasovskii functional method. Finally, a numerical simulation is provided to show the effectiveness of the proposed approach.

Synchronization of Uncertain Neural Networks with H8 Performance and Mixed Time-Delays

2011 ◽  
pp. 1208-1232
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

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 Exponential Stability and Guaranteed Cost of Switched Linear Systems with Mixed Time-Varying Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Time Delays ◽  
Functional Method ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Mixed Time Delays ◽  
Guaranteed Cost ◽  
Lyapunov Functional Method ◽  
Delay Dependent

This paper deals with the problems of exponential stability and guaranteed cost of switched linear systems with mixed time delays. Based on Lyapunov functional method, we present new delay-dependent conditions that guarantee both the exponential stability and an upper bound for some performance index. The criteria are delay-dependent conditions and are given in terms of linear matrix inequalities. Numerical examples are provided to illustrate the effectiveness of the results.

scholarly journals Globalμ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaofeng Chen ◽  
Qiankun Song ◽  
Yurong Liu ◽  
Zhenjiang Zhao
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Distributed Delay ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Weighting Matrix ◽  
Homeomorphism Mapping ◽  
Delay Dependent ◽  
Complex Valued

The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the globalμ-stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.

scholarly journals Dynamical Analysis for High-Order Delayed Hopfield Neural Networks with Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Dengwang Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Dynamical Analysis ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Linear Matrix Inequality Approach ◽  
Lyapunov Functional Method

The global exponential stability and uniform stability of the equilibrium point for high-order delayed Hopfield neural networks with impulses are studied. By utilizing Lyapunov functional method, the quality of negative definite matrix, and the linear matrix inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. Two examples are also given to illustrate the effectiveness of our results.

The Globally Asymptotic Stability Analysis of the Delayed Recurrent Neural Networks Stability Criterion via LMI Technique and Nonsmooth Analysis

2013 ◽  
Vol 380-384 ◽  
pp. 2030-2033
Author(s):  
Zhen Cai Li ◽  
Yang Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Recurrent Neural Networks ◽  
Nonsmooth Analysis ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotic Stability ◽  
Lyapunov Functional Method

This paper considers the problem of globally asymptotic stability of the recurrent neural networks with time-varying delays. A linear matrix inequality (LMI) technology and Lyapunov functional method is employed by combing the means of the nonsmooth analysis. A few new sufficient conditions and criterions were proposed to ensure the delayed recurrent neural networks are uniqueness and globally asymptotic stability of their equilibrium point. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.

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