Global synchronization of discrete-time coupled neural networks with Markovian switching and impulses

2016 ◽  
Vol 09 (03) ◽  
pp. 1650041 ◽  
Author(s):  
Jie Tan ◽  
Chuandong Li
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Global Synchronization ◽  
Discrete State ◽  
Coupled Neural Networks ◽  
Software Packages ◽  
Linear Matrix Inequality Approach ◽  
Impulsive Disturbances

This paper is concerned with the problem of synchronization analysis for discrete-time coupled neural networks. The networks under consideration are subject to: (1) the jumping parameters that are modeled as a continuous-time, discrete-state Markov process; (2) impulsive disturbances; and (3) time delays that include both the mode-dependent discrete and distributed delay. By constructing suitable Lyapunov–Krasovskii functional and combining with linear matrix inequality approach, several novel criteria are derived for verifying the global exponential synchronization in the mean square of such stochastic dynamical networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. A simulation example is presented to show the effectiveness and applicability of the obtained 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 Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xinsong Yang ◽  
Mengzhe Zhou ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Distributed Delay ◽  
Transmission Efficiency ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Coupled Neural Networks ◽  
Time Varying Delay ◽  
Unbounded Distributed Delays ◽  
Varying Delay

This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Global synchronization for hybrid coupled neural networks with interval time-varying delays: A matrix-based quadratic convex approach

2016 ◽  
Vol 10 (02) ◽  
pp. 1750025
Author(s):  
Thongchai Botmart ◽  
Narongsak Yotha ◽  
Kanit Mukdasai ◽  
Supreecha Wongaree
Keyword(s):  
Neural Networks ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Global Synchronization ◽  
Interval Time ◽  
Coupled Neural Networks ◽  
Time Varying Delay

This paper is concerned with the global synchronization problems for coupled neural networks (NNs) with hybrid coupling and interval time-varying delays. An appropriate Lyapunov–Krasovskii functional (LKF) and Kronecker product properties are used to form some new delay-dependent synchronization conditions in terms of linear matrix inequalities. A matrix-based quadratic convex approach introduce for sufficient conditions to ensure global synchronization where the time-varying delay is continuous uniformly bounded and its time-derivative bounded by upper and lower bounds. Simulation results are given to show the effectiveness and benefits of the proposed methods.

GLOBAL SYNCHRONIZATION IN AN ARRAY OF DISCRETE-TIME NEURAL NETWORKS WITH NONLINEAR COUPLING AND TIME-VARYING DELAYS

2009 ◽  
Vol 19 (01) ◽  
pp. 57-63 ◽  
Author(s):  
JINLING LIANG ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Coupled Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Coupling ◽  
Global Synchronization ◽  
Synchronization Scheme

A general model for an array of discrete-time neural networks with hybrid coupling is proposed, which is composed of nonlinear coupling and time-varying delays. The coupling terms are described in terms of Lipchitz-type conditions that reflect more realistic dynamical behaviors of coupled systems in practice. The properties of Kronecker product are employed in order to pursue mathematical simplicity of dynamics analysis. On the basis of Lyapunov stability theory, an effective matrix functional is utilized to establish sufficient conditions under which the considered neural networks are globally synchronized. These conditions, which are dependent on the lower bound and the upper bound of the time-varying time delays, are expressed in terms of several linear matrix inequalities (LMIs), and therefore can be easily verified by utilizing the numerically efficient Matlab LMI toolbox. One illustrative example is given to justify the validity and feasibility of the proposed synchronization scheme.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

SYNCHRONIZATION IN AN ARRAY OF HYBRID COUPLED NEURAL NETWORKS WITH MODE-DEPENDENT MIXED DELAYS AND MARKOVIAN SWITCHING

2009 ◽  
Vol 23 (09) ◽  
pp. 1171-1187 ◽  
Author(s):  
YANG TANG ◽  
RUNHE QIU ◽  
JIAN-AN FANG
Keyword(s):  
Neural Networks ◽  
Transition Probability ◽  
Distributed Delay ◽  
Mode Switching ◽  
Mixed Delays ◽  
Time Varying ◽  
Chaotic Neural Networks ◽  
Coupled Neural Networks ◽  
Hybrid Coupling ◽  
Coupling Time

In this letter, a general model of an array of N linearly coupled chaotic neural networks with hybrid coupling is proposed, which is composed of constant coupling, time-varying delay coupling and distributed delay coupling. The complex network jumps from one mode to another according to a Markovian chain with known transition probability. Both the coupling time-varying delays and the coupling distributed delays terms are mode-dependent. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization in an array of jump chaotic neural networks with mode-dependent hybrid coupling and mixed delays in mean square. Finally, numerical simulations illustrated by mode switching between two complex networks of different structure dependent on mode switching verify the effectiveness of the proposed results.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

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