scholarly journals Synchronization Control for Stochastic Neural Networks with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Qing Zhu ◽  
Aiguo Song ◽  
Shumin Fei ◽  
Yuequan Yang ◽  
Zhiqiang Cao
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Synchronization Control ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square Stability ◽  
Control Gain ◽  
Control Scheme

Synchronization control of stochastic neural networks with time-varying discrete and continuous delays has been investigated. A novel control scheme is proposed using the Lyapunov functional method and linear matrix inequality (LMI) approach. Sufficient conditions have been derived to ensure the global asymptotical mean-square stability for the error system, and thus the drive system synchronizes with the response system. Also, the control gain matrix can be obtained. With these effective methods, synchronization can be achieved. Simulation results are presented to show the effectiveness of the theoretical results.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

Ultimate Boundedness of Stochastic Neural Networks with Delays

2011 ◽  
Vol 204-210 ◽  
pp. 1549-1552
Author(s):  
Li Wan ◽  
Qing Hua Zhou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Functional ◽  
Signal Transmission ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness

Although ultimate boundedness of several classes of neural networks with constant delays was studied by some researchers, the inherent randomness associated with signal transmission was not taken account into these networks. At present, few authors study ultimate boundedness of stochastic neural networks and no related papers are reported. In this paper, by using Lyapunov functional and linear matrix inequality, some sufficient conditions ensuring the ultimate boundedness of stochastic neural networks with time-varying delays are established. Our criteria are easily tested by Matlab LMI Toolbox. One example is given to demonstrate our criteria.

Mean Square Asymptotic Stability of Neutral Stochastic Neutral Networks with Multiple Time-Varying Delays

2013 ◽  
Vol 684 ◽  
pp. 579-582
Author(s):  
Xiang Dong Shi
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Multiple Time ◽  
Time Varying ◽  
Lyapunov Functional Method ◽  
Inequality Techniques ◽  
Neutral Stochastic Neural Networks

The paper considers the problems of almost surely asymptotic stability for neutral stochastic neural networks with multiple time-varying delays. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and almost surely asymptotic stability of neutral stochastic neural networks with multiple time-varying delays are established. The results are shown to be generalizations of some previously published results and are less conservative than existing 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.

scholarly journals Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 742 ◽  
Author(s):  
Pharunyou Chanthorn ◽  
Grienggrai Rajchakit ◽  
Jenjira Thipcha ◽  
Chanikan Emharuethai ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Equivalent Representation ◽  
Stochastic Effects ◽  
Complex Valued

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

scholarly journals Globalμ-Stability Analysis for Impulsive Stochastic Neural Networks with Unbounded Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lizi Yin ◽  
Xinchun Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Delays ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Software Packages ◽  
The Mean ◽  
Theoretical Results

We investigate the globalμ-stability in the mean square of impulsive stochastic neural networks with unbounded time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, a novel robust stability condition, in the form of linear matrix inequalities, is derived. These sufficient conditions can be tested by MATLAB LMI software packages. The results extend and improve the earlier publication. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Synchronization of decentralized event-triggered uncertain switched neural networks with two additive time-varying delays

2020 ◽  
Vol 25 (2) ◽  
Author(s):  
Rajarathinam Vadivel ◽  
M. Syed Ali ◽  
Faris Alzahrani ◽  
Jinde Cao ◽  
Young Hoon Joo
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Switched Neural Networks ◽  
Central Controller ◽  
Event Triggered

This paper addresses the problem of synchronization for decentralized event-triggered uncertain switched neural networks with two additive time-varying delays. A decentralized eventtriggered scheme is employed to determine the time instants of communication from the sensors to the central controller based on narrow possible information only. In addition, a class of switched neural networks is analyzed based on the Lyapunov–Krasovskii functional method and a combined linear matrix inequality (LMI) technique and average dwell time approach. Some sufficient conditions are derived to guarantee the exponential stability of neural networks under consideration in the presence of admissible parametric uncertainties. Numerical examples are provided to illustrate the effectiveness of the obtained results. 

ON PASSIVITY ANALYSIS OF STOCHASTIC DELAYED NEURAL NETWORKS WITH RANDOM ABRUPT CHANGES

2007 ◽  
Vol 03 (03) ◽  
pp. 321-330 ◽  
Author(s):  
XU-YANG LOU ◽  
BAO-TONG CUI
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequality ◽  
Delayed Neural Networks ◽  
Passivity Analysis ◽  
Abrupt Changes

The passivity conditions for stochastic neural networks with time-varying delays and random abrupt changes are considered in this paper. Sufficient conditions on passivity of stochastic neural networks with time-varying delays and random abrupt changes are developed in the linear matrix inequality (LMI) setting. The results obtained in this paper improve and extend some of the previous results.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

On Robust Stability for Stochastic Neural Networks of Neutral-Type with Uncertainties and Time-Varying Delays

2012 ◽  
Vol 457-458 ◽  
pp. 716-722
Author(s):  
Guo Quan Liu ◽  
Simon X. Yang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Stability Criteria ◽  
Analysis Problem ◽  
Analysis Technique ◽  
Robust Stability Analysis

This paper is concerned with the robust stability analysis problem for stochastic neural networks of neutral-type with uncertainties and time-varying delays. Novel stability criteria are proposed in terms of linear matrix inequality (LMI) by defining a Lyapunov-Krasovskii functional and using the stochastic analysis technique. Two examples are given to show the effectiveness of the obtained conditions.

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