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 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 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 New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei Kang ◽  
Jun Cheng ◽  
Xiangyang Cheng
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals New Results on Passivity Analysis of Delayed Discrete-Time Stochastic Neural Networks

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Jianjiang Yu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay is investigated. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. Two numerical examples are given to show the effectiveness and the benefits 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 A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

scholarly journals Novel Stability Analysis for Uncertain Neutral-Type Lur’e Systems with Time-Varying Delays Using New Inequality

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yanmeng Wang ◽  
Lianglin Xiong ◽  
Yongkun Li ◽  
Haiyang Zhang ◽  
Chen Peng
Keyword(s):  
Stability Analysis ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
New Class ◽  
Inequality Techniques ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper considers the delay-dependent stability analysis of neutral-type Lur’e systems with time-varying delays and sector bounded nonlinearities. First of all, using constructed function methods, a new Jensen-like inequality is introduced to obtain less conservative results. Second, a new class of Lyapunov-Krasovskii functional (LKF) is constructed according to the characteristic of the considered systems. Third, combining with the new inequality and reciprocal convex approach and some other inequality techniques, the new less conservative robust stability criteria are shown in the form of linear matrix inequalities (LMIs). Finally, three examples demonstrate the feasibility and the superiority of our methods.

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.

Robust Stability Analysis of Delayed Stochastic Neural Networks via Wirtinger-Based Integral Inequality

2021 ◽  
Vol 33 (1) ◽  
pp. 227-243
Author(s):  
R. Suresh ◽  
A. Manivannan
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Uncertain Stochastic Neural Networks ◽  
Delay Dependent ◽  
The Given

We discuss stability analysis for uncertain stochastic neural networks (SNNs) with time delay in this letter. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and utilizing Wirtinger inequalities for estimating the integral inequalities, the delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs). We discuss the parameter uncertainties in terms of norm-bounded conditions in the given interval with constant delay. The derived conditions ensure that the global, asymptotic stability of the states for the proposed SNNs. We verify the effectiveness and applicability of the proposed criteria with numerical examples.

CLUSTER SYNCHRONIZATION OF DISCRETE-TIME STOCHASTIC COMPLEX DYNAMICAL NETWORKS WITH PROBABILISTIC INTERVAL TIME-VARYING DELAYS

2012 ◽  
Vol 26 (05) ◽  
pp. 1250037 ◽  
Author(s):  
HONGJIE LI
Keyword(s):  
Discrete Time ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Nonlinear Functions ◽  
Interval Time ◽  
Analysis Techniques ◽  
Binary Switch ◽  
Delay Dependent

The paper investigates the cluster synchronization in discrete-time complex networks with stochastic nonlinearities and probabilistic interval time-varying delays. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities. The solvability of derived conditions depends on not only the probability of the binary switch between nonlinear functions, but also the size of the delay and the probability of the delay taking values in some intervals. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed criterion.

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