scholarly journals On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

scholarly journals On Less Conservative Stability Criteria for Neural Networks with Time-Varying Delays Utilizing Wirtinger-Based Integral Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Integral Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Maximum Delay ◽  
Delay Dependent

This paper investigates the problem of stability analysis for neural networks with time-varying delays. By utilizing the Wirtinger-based integral inequality and constructing a suitable augmented Lyapunov-Krasovskii functional, two less conservative delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). Three numerical examples are included to explain the superiority of the proposed methods by comparing maximum delay bounds with the recent results published in other literature.

scholarly journals Novel extended dissipativity criteria for generalized neural networks with interval discrete and distributed time-varying delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sunisa Luemsai ◽  
Thongchai Botmart ◽  
Wajaree Weera
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Integral Inequality ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Numerical Examples ◽  
Combination Technique ◽  
Generalized Neural Networks ◽  
Special Case

AbstractThe problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended dissipativity criteria are achieved for the generalized neural networks with interval discrete and distributed time-varying delays. By the above methods, the less conservative asymptotic stability criteria are obtained for a special case of the generalized neural networks. By using the Matlab LMI toolbox, the derived new asymptotic stability and extended dissipativity criteria are expressed in terms of linear matrix inequalities (LMIs) that cover $H_{\infty }$ H ∞ , $L_{2}$ L 2 –$L_{\infty }$ L ∞ , passivity, and dissipativity performance by setting parameters in the general performance index. Finally, we show numerical examples which are less conservative than other examples in the literature. Moreover, we present numerical examples for asymptotic stability and extended dissipativity performance of the generalized neural networks, including a special case of the generalized neural networks.

IMPROVED RESULTS ON STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS: NOVEL DELAY-DEPENDENT CRITERIA

2010 ◽  
Vol 24 (08) ◽  
pp. 775-789 ◽  
Author(s):  
O. M. KWON ◽  
S. M. LEE ◽  
JU H. PARK
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Analysis Techniques ◽  
The Neural Networks ◽  
Delay Dependent

In this paper, the problem of stability analysis of neural networks with discrete time-varying delays is considered. By constructing a new Lyapunov functional and some novel analysis techniques, new delay-dependent criteria for checking the asymptotic stability of the neural networks are established. The criteria are presented in terms of linear matrix inequalities, which can be easily solved and checked by various convex optimization algorithms. Three numerical examples are included to show the superiority of our results.

scholarly journals Analysis on Passivity for Uncertain Neural Networks with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Uncertain Neural Networks

The problem of passivity analysis for neural networks with time-varying delays and parameter uncertainties is considered. By the consideration of newly constructed Lyapunov-Krasovskii functionals, improved sufficient conditions to guarantee the passivity of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum allowable delay bounds.

RELAXED STABILITY CONDITIONS FOR DELAYED RECURRENT NEURAL NETWORKS WITH POLYTOPIC UNCERTAINTIES

2006 ◽  
Vol 16 (06) ◽  
pp. 473-482 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YUN ZOU
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Polytopic Uncertainties ◽  
Parameter Dependent

This paper investigates the problem of stability analysis for recurrent neural networks with time-varying delays and polytopic uncertainties. Parameter-dependent Lypaunov functionals are employed to obtain sufficient conditions that guarantee the robust global exponential stability of the equilibrium point of the considered neural network. The derived stability criteria are expressed in terms of a set of relaxed linear matrix inequalities, which can be easily tested by using commercially available software. Two numerical examples are provided to demonstrate the effectiveness of the proposed 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.

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.

scholarly journals Passivity of Memristive BAM Neural Networks with Probabilistic and Mixed Time-Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-25
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao
Keyword(s):  
Neural Networks ◽  
Probability Distribution ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bernoulli Distribution ◽  
Matrix Inequalities ◽  
Bidirectional Associative Memory ◽  
Leakage Delays ◽  
Numerical Examples

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
C. Emharuethai ◽  
P. Niamsup
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

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