A PASSIVITY APPROACH TO SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (29) ◽  
pp. 3531-3541 ◽  
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Optimization Problem ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Convex Optimization Problem ◽  
Synchronization Problem ◽  
Error System

In this letter, we propose a new passivity-based synchronization method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory and linear matrix inequality (LMI) approach, the passivity-based controller is presented to make the synchronization error system for time-delayed chaotic systems not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the synchronization problem for chaotic delayed Hopfield neural networks is investigated.

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.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

scholarly journals Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Fang ◽  
Kang Yan ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Impulsive Synchronization ◽  
Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

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.

Delay-Range-Dependent Robust Stability for Uncertain Stochastic Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2 (4) ◽  
pp. 45-59
Author(s):  
Wei Feng ◽  
Haixia Wu
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Optimization Problem ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Stability Criteria ◽  
Convex Optimization Problem ◽  
Robust Stability Analysis ◽  
Uncertain Stochastic Neural Networks

This paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. By utilizing a Lyapunov-Krasovskii functional and conducting stochastic analysis, the authors show that the addressed neural networks are globally, robustly, and asymptotically stable if a convex optimization problem is feasible. Some stability criteria are derived for all admissible uncertainties, and these stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Five numerical examples are given to demonstrate the usefulness of the proposed robust stability criteria.

$\mathcal{H}_{\infty}$ LAG SYNCHRONIZATION FOR CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (21) ◽  
pp. 2801-2812 ◽  
Author(s):  
CHOON KI AHN
Keyword(s):  
Chaotic Systems ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Lag Synchronization ◽  
Convex Optimization Problem ◽  
Synchronization Problem ◽  
Norm Constraint ◽  
Synchronization Scheme ◽  
New Formula

In this paper, we propose a new [Formula: see text] lag synchronization scheme for a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, the [Formula: see text] lag synchronization controller is presented to not only guarantee exponential lag synchronization but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the [Formula: see text] lag synchronization problem for Genesio–Tesi system is investigated.

scholarly journals Robust H-infinity State Estimation of Uncertain Neural Networks with Two Additive Time-Varying Delays

2020 ◽  
Author(s):  
Xiaoping Hu ◽  
Yajun Wang ◽  
Jiakai Ding ◽  
Dongming Xiao
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Uncertain Neural Networks ◽  
Error System

This study is mainly concerned with the problem of robust H∞ state estimation of uncertain neural networks with two additive time-varying delays. A novel linear matrix inequalities (LMIs) is constructed based on Lyapunov-Krasovskii functionals (LKFs) which contains two additive time-varying delays components. LMIs method are used to estimate the derivative of LKFs, it is calculated that the derivative of the LKFs is smaller than zero, which proved that uncertain neural networks with two additive time-varying delays is globally asymptotically stable. Meantime, a stability criterion of error system is presented such that the HâĹđ performance is guaranteed. Finally, two numerical simulation examples have been performed to demonstrate the effectiveness of developed approach.

scholarly journals Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinde Cao ◽  
Abdulaziz Alofi ◽  
Abdullah Al-Mazrooei ◽  
Ahmed Elaiw
Keyword(s):  
Neural Networks ◽  
Matrix Measure ◽  
Chaotic Neural Networks ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Arbitrary Switching ◽  
Parameters Uncertainty ◽  
Inequality Technique ◽  
Error System ◽  
Switched Interval Networks

This paper investigates synchronization problem of switched delay networks with interval parameters uncertainty, based on the theories of the switched systems and drive-response technique, a mathematical model of the switched interval drive-response error system is established. Without constructing Lyapunov-Krasovskii functions, introducing matrix measure method for the first time to switched time-varying delay networks, combining Halanay inequality technique, synchronization criteria are derived for switched interval networks under the arbitrary switching rule, which are easy to verify in practice. Moreover, as an application, the proposed scheme is then applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

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.

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