scholarly journals Impulsive Synchronization of Nonlinearly Coupled Complex Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Guizhen Feng ◽  
Jinde Cao ◽  
Jianquan Lu
Keyword(s):  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Sufficient Condition ◽  
Impulsive Synchronization ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Objective State ◽  
The Stability ◽  
Low Dimensional ◽  
Average Impulsive Interval

This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive interval. A numerical example is given to illustrate the effectiveness and feasibility of the proposed methods and results.

scholarly journals Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Limin Zou ◽  
Yang Peng ◽  
Yuming Feng ◽  
Zhengwen Tu
Keyword(s):  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Impulsive Synchronization ◽  
Chaotic Circuits ◽  
The Stability ◽  
Control And Synchronization

The purpose of this note is to study impulsive control and synchronization of memristor based chaotic circuits shown by Muthuswamy. We first establish a less conservative sufficient condition for the stability of memristor based chaotic circuits. After that, we discuss the effect of errors on stability. Meanwhile, we also discuss impulsive synchronization of two memristor based chaotic systems. Our results are more general and more applicable than the ones shown by Yang, Li, and Huang. Finally, several numerical examples are given to show the effectiveness of our methods.

scholarly journals Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi-Wei Liu ◽  
Zhi-Hong Guan ◽  
Hong Zhou
Keyword(s):  
Multiagent System ◽  
Impulsive Control ◽  
Sampling Period ◽  
Switching Topology ◽  
Sufficient Condition ◽  
Leader Following ◽  
Fixed Topology ◽  
The Stability ◽  
Sampling Instant ◽  
Necessary And Sufficient

This paper studied the consensus problem of the leader-following multiagent system. It is assumed that the state information of the leader is only available to a subset of followers, while the communication among agents occurs at sampling instant. To achieve leader-following consensus, a class of distributed impulsive control based on sampling information is proposed. By using the stability theory of impulsive systems, algebraic graph theory, and stochastic matrices theory, a necessary and sufficient condition for fixed topology and sufficient condition for switching topology are obtained to guarantee the leader-following consensus of the multiagent system. It is found that leader-following consensus is critically dependent on the sampling period, control gains, and interaction graph. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach and the correctness of theoretical analysis.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

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.

Pinning Impulsive Synchronization of Fractional Complex Dynamical Networks

2015 ◽  
Author(s):  
Weiyuan Ma ◽  
Changpin Li ◽  
Yujiang Wu
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Impulsive Synchronization ◽  
Pinning Impulsive Control

In this paper, a class of fractional complex dynamical networks is synchronized via pinning impulsive control. At first, a comparison principle is established for fractional impulsive differential equations. Then the synchronization criterion is obtained by using the derived comparison principle. Examples are given to illustrate the results.

scholarly journals A Generalization of the Cauchy-Schwarz Inequality and Its Application to Stability Analysis of Nonlinear Impulsive Control Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Peng ◽  
Jiang Wu ◽  
Limin Zou ◽  
Yuming Feng ◽  
Zhengwen Tu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Impulsive Control ◽  
Schwarz Inequality ◽  
Sufficient Condition ◽  
Numerical Example ◽  
Impulsive Control Systems ◽  
The Stability

In this paper, we first present a generalization of the Cauchy-Schwarz inequality. As an application of our result, we obtain a new sufficient condition for the stability of a class of nonlinear impulsive control systems. We end up this note with a numerical example which shows the effectiveness of our method.

scholarly journals Synchronization of Time Delay Coupled Neural Networks Based on Impulsive Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jie Fang ◽  
Yin Zhang ◽  
Danying Xu ◽  
Junwei Sun
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Control Method ◽  
Impulsive Control ◽  
Lyapunov Stability Theory ◽  
Control Effect ◽  
Coupled Neural Networks ◽  
Impulsive Synchronization ◽  
The Stability ◽  
Delayed Impulses

This paper investigates the impulsive synchronization of time delay coupled neural networks. Based on the Lyapunov stability theory and impulsive control method, a distributed delayed impulsive controller is designed to realize synchronization of the coupled neural networks. A new impulsive delayed inequality is proposed, where the control effect of distributed delayed impulses is fully considered. In addition, a suitable Lyapunov-like function is established to prove the stability of the synchronization system. Numerical simulation examples are introduced to illustrate the effectiveness and feasibility of the main results.

scholarly journals Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiuli Chai ◽  
Zhihua Gan ◽  
Chunxiao Shi
Keyword(s):  
Dynamical Systems ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Control Scheme ◽  
Functional Differential ◽  
Invariant Principle

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

scholarly journals Impulsive Synchronization of Chaotic Lur'e Systems by Measurement Feedback

1998 ◽  
Vol 08 (06) ◽  
pp. 1371-1381 ◽  
Author(s):  
J. A. K. Suykens ◽  
T. Yang ◽  
L. O. Chua
Keyword(s):  
Impulsive Control ◽  
Dynamic Measurement ◽  
Hyperchaotic System ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Control Laws ◽  
Impulsive Synchronization ◽  
Chaotic Lur’E Systems ◽  
Measurement Feedback

In this paper we consider impulsive control of master-slave synchronization schemes that consist of identical Lur'e systems. Impulsive control laws are investigated which make use of linear or nonlinear dynamic measurement feedback. A sufficient condition for global asymptotic stability is presented which is characterized by a set of matrix inequalities. Synchronization is proven for the error between the output signals. The method is illustrated on Chua's circuit and a hyperchaotic system with coupled Chua's circuits.

IMPULSIVE CONTROL FOR T–S FUZZY SYSTEM AND ITS APPLICATION TO CHAOTIC SYSTEMS

2006 ◽  
Vol 16 (08) ◽  
pp. 2417-2423 ◽  
Author(s):  
YAN-WU WANG ◽  
ZHI-HONG GUAN ◽  
HUA O. WANG ◽  
JIANG-WEN XIAO
Keyword(s):  
Chaotic System ◽  
Fuzzy System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Structure ◽  
Impulsive Control ◽  
Fuzzy Model ◽  
Chua's Circuit ◽  
Control Scheme ◽  
The Stability

An impulsive T–S fuzzy model is presented in this paper. The stability of impulsive controlled T–S fuzzy system has been analyzed theoretically. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the stabilization of T–S fuzzy system. Some typical chaotic systems, such as Chua's circuit, Lorenz system and Chen's chaotic system, are considered as illustrations to demonstrate the effectiveness of the proposed control scheme.

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