scholarly journals Passivity and Synchronization of Multiple Multi-Delayed Neural Networks via Impulsive Control

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong Wang ◽  
Zhichun Yang ◽  
Tonglai Liu ◽  
Hong-An Tang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Lyapunov Functional ◽  
Impulsive Control ◽  
Time Dependent ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delayed Neural Networks ◽  
Theoretical Results

This paper is concerned with the passivity and synchronization for multiple multi-delayed neural networks (MMDNNs) under impulsive control. To ensure the passivity, input strict passivity, and output strict passivity in MMDNNs, a suitable impulsive controller is designed. Moreover, an impulsive time-dependent Lyapunov functional is exploited to obtain the synchronization criterion of MMDNNs, where the criterion is formulated by linear matrix inequalities. Numerical examples are given to verify the validity of the theoretical results.

Synchronization of delayed neural networks with hybrid coupling via impulsive control

2019 ◽  
Vol 41 (13) ◽  
pp. 3714-3724 ◽  
Author(s):  
Tianhu Yu ◽  
Huamin Wang ◽  
Dengqing Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Upper Bound ◽  
Hybrid Control ◽  
Impulsive Control ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Delayed Neural Networks ◽  
Coupled Neural Networks

The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.

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.

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.

Passivity of memristive BAM neural networks with leakage and additive time-varying delays

2018 ◽  
Vol 32 (04) ◽  
pp. 1850041 ◽  
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao ◽  
...  
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Matrix Inequalities ◽  
Leakage Delays ◽  
Delay Dependent ◽  
Theoretical Results

This paper investigates the passivity of memristive bidirectional associate memory neural networks (MBAMNNs) with leakage and additive time-varying delays. Based on some useful inequalities and appropriate Lyapunov–Krasovskii functionals (LKFs), several delay-dependent conditions for passivity performance are obtained in linear matrix inequalities (LMIs). Moreover, the leakage delays as well as additive delays are considered separately. Finally, numerical simulations are provided to demonstrate the feasibility of the theoretical results.

NOVEL ROBUST DELAY-DEPENDENT CRITERION FOR ABSOLUTE STABILITY OF LUR'E SYSTEMS OF NEUTRAL TYPE

2009 ◽  
Vol 23 (13) ◽  
pp. 1641-1650 ◽  
Author(s):  
S. M. LEE ◽  
O. M. KWON ◽  
JU H. PARK
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functional ◽  
Absolute Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Numerical Examples ◽  
Delay Dependent

This letter considers uncertain Lur'e systems of neutral type with sector and slope restrictions. By constructing a new Lyapunov functional, a novel delay-dependent criterion for absolute stability is derived in terms of linear matrix inequalities (LMIs). Two numerical examples are illustrated 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 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 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.

AUTOASSOCIATIVE MEMORY DESIGN USING INTERCONNECTED GENERALIZED BRAIN-STATE-IN-A-BOX NEURAL NETWORKS

2005 ◽  
Vol 15 (03) ◽  
pp. 181-196 ◽  
Author(s):  
CHEOLHWAN OH ◽  
STANISLAW H. ŻAK ◽  
GUISHENG ZHAI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Brain State ◽  
Stability Conditions ◽  
Network Architectures ◽  
Associative Memories ◽  
Matrix Inequalities ◽  
Memory Design

A class of interconnected neural networks composed of generalized Brain-State-in-a-Box (gBSB) neural subnetworks is considered. Interconnected gBSB neural network architectures are proposed along with their stability conditions. The design of the interconnected neural networks is reduced to the problem of solving linear matrix inequalities (LMIs) to determine the interconnection parameters. A method for solving LMIs is devised generating the solutions that, in general, are further away from zero than the corresponding solutions obtained using MATLAB's LMI toolbox, thus resulting in stronger interconnections between the subnetworks. The proposed architectures are then used to construct neural associative memories. Simulations are performed to illustrate the results obtained.

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