scholarly journals Synchronization of Switched Complex Bipartite Neural Networks with Infinite Distributed Delays and Derivative Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Qiuxiang Bian ◽  
Jinde Cao ◽  
Jie Wu ◽  
Hongxing Yao ◽  
Tingfang Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Derivative Coupling ◽  
Infinite Distributed Delays ◽  
Theoretical Results

A new model of switched complex bipartite neural network (SCBNN) with infinite distributed delays and derivative coupling is established. Using linear matrix inequality (LMI) approach, some synchronization criteria are proposed to ensure the synchronization between two SCBNNs by constructing effective controllers. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

scholarly journals Dynamical Behaviors of Stochastic Hopfield Neural Networks with Both Time-Varying and Continuously Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Qinghua Zhou ◽  
Penglin Zhang ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Functional Theory ◽  
Dynamical Behaviors ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Hopfield neural networks with both time-varying and continuously distributed delays. By employing the Lyapunov functional theory and linear matrix inequality, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, an example is given to illustrate the correctness and effectiveness of our theoretical results.

SYNCHRONIZATION OF NEURAL NETWORKS OF NEUTRAL TYPE WITH STOCHASTIC PERTURBATION

2009 ◽  
Vol 23 (14) ◽  
pp. 1743-1751 ◽  
Author(s):  
JU H. PARK ◽  
O. M. KWON
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Method ◽  
Controller Design ◽  
Neutral Type ◽  
Stochastic Perturbation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Existence Criterion

In this letter, the problem of feedback controller design to achieve synchronization for neural network of neutral type with stochastic perturbation is considered. Based on Lyapunov method and LMI (linear matrix inequality) framework, the goal of this letter is to derive an existence criterion of the controller for the synchronization between master and response networks.

Cellular Neural Network Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization for Noise Removal of Color Image

2011 ◽  
Vol 422 ◽  
pp. 771-774
Author(s):  
Te Jen Su ◽  
Jui Chuan Cheng ◽  
Yu Jen Lin
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Linear Matrix Inequality ◽  
Color Image ◽  
Particle Swarm ◽  
Cellular Neural Network ◽  
Noise Removal ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Swarm Optimization

This paper presents a color image noise removal technique that employs a cellular neural network (CNN) based on hybrid linear matrix inequality (LMI) and particle swarm optimization (PSO). For designing templates of CNN, the Lyapunov stability theorem is applied to derive the criterion for the uniqueness and global asymptotic stability of the CNN’s equilibrium point. The template design is characterized as a standard LMI problem, and the parameters of templates are optimized by PSO. The input templates are obtained by employing the CNN’s property of saturation nonlinearity, which can be used to eliminate noise from arbitrary corrupted images. The demonstrated examples are compared favorably with other available methods, which illustrate the better performance of the proposed LMI-PSO-CNN methodology.

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.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

Stability Criterion of Discrete Hopfield Neural Networks with Multiple Delays in Parallel Mode: Linear Matrix Inequality

2011 ◽  
Vol 225-226 ◽  
pp. 1270-1273
Author(s):  
Xiao Feng Lai ◽  
Xing Yin ◽  
Hai Yang Zou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Stability Criterion ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Parallel Mode

In this paper, Discrete Hopfield Neural Networks with Multple Delays is introduced.And a stability criterion of Discrete Hopfield Neural Networks with Multple Delays is studied bythe linear matrix inequality. It provides a theory basis for the application of Discrete Hopfield Neural Networks with Multple Delays.

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

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