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 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.

Impulsive Control and Synchronization of Memristor-Based Chaotic Circuits

2014 ◽  
Vol 24 (12) ◽  
pp. 1450162 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Memory Function ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Circuit Element ◽  
Chaotic Circuits ◽  
Control And Synchronization ◽  
Passive Circuit

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented.

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.

scholarly journals The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Numerical Examples ◽  
Single Output ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

This paper investigates the stabilization and synchronization of a class of fractional-order chaotic systems which are affected by external disturbances. The chaotic systems are assumed that only a single output can be used to design the controller. In order to design the proper controller, some observer systems are proposed. By using the observer systems some sufficient conditions for achieving chaos control and synchronization of fractional-order chaotic systems are derived. Numerical examples are presented by taking the fractional-order generalized Lorenz chaotic system as an example to show the feasibility and validity of the proposed method.

SYNCHRONIZATION OF IMPULSIVELY COUPLED SYSTEMS

2008 ◽  
Vol 18 (05) ◽  
pp. 1539-1549 ◽  
Author(s):  
XIUPING HAN ◽  
JUN-AN LU ◽  
XIAOQUN WU
Keyword(s):  
Dynamical Systems ◽  
Control Strategy ◽  
Impulsive Control ◽  
Coupled Model ◽  
Coupled Systems ◽  
Single System ◽  
Impulsive Synchronization ◽  
The Past ◽  
Impulsive Control Strategy ◽  
Control And Synchronization

In the past years, impulsive control for a single system and impulsive synchronization between two systems have been extensively studied. However, investigation on impulsive control and synchronization of complex networks has just started. In these studies, a network is continuously coupled, and then is synchronized by using impulsive control strategy. In this paper, a new and different coupled model is proposed, where the systems are coupled only at discrete instants through impulsive connections. Several criteria for synchronizing such kind of impulsively coupled complex dynamical systems are established. Two examples are also worked through for illustrating the main results.

scholarly journals Delayed impulive SDEs driven by multiplicative fBm noise and additive fBm noise

2021 ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Xiu Liu ◽  
Jinde Cao ◽  
Changfeng Xue
Keyword(s):  
Chaotic Systems ◽  
Impulsive Control ◽  
Chaotic Oscillator ◽  
Mean Square ◽  
Ultimate Boundedness ◽  
Response System ◽  
Pth Moment Exponential Stability ◽  
The Stability ◽  
Moment Exponential Stability ◽  
Lyapunov Technique

The stability and boundedness for delayed impulsive SDEs driven by fBm are studied in this paper. Two kinds of noises, i.e, additive fBm noise and mul-tiplicative fBm noise are both taken into consideration. By using stochastic Lyapunov technique and impulsive control theory, sufficient criteria for pth moment exponential stability and mean square ultimate boundedness are derived, for two kinds of fBm driven delayed impulsive SDEs, respectively. As application, the obtained results are used to do practical synchronization w.r.t. a class of chaotic systems, in which the response system is perturbed by additive fBm noises. Finally, A Chua chaotic oscillator is given to verify the validity and applicability of the derived 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 On the Impulsive Synchronization Control for a Class of Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Bo Wang ◽  
Peng Shi ◽  
Xiucheng Dong
Keyword(s):  
Numerical Simulation ◽  
Control Theory ◽  
Lyapunov Functional ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Synchronization Control ◽  
Practical Application ◽  
Impulsive Synchronization ◽  
Theoretical Results

The problem on chaos synchronization for a class of chaotic system is addressed. Based on impulsive control theory and by constructing a novel Lyapunov functional, new impulsive synchronization strategies are presented and possess more practical application value. Finally some typical numerical simulation examples are included to demonstrate the effectiveness of the theoretical results.

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