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.

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.

Asymptotical Synchronization of Lur'e Systems Using Network Reliable Control

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
R. Rakkiyappan ◽  
S. Lakshmanan ◽  
C. P. Lim
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Reliable Control ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Chaotic Lur’E Systems ◽  
Error System ◽  
Theoretical Results

This paper presents the synchronization criteria for two identical delayed chaotic Lur'e systems. Here, we employ network reliable feedback control for achieving synchronization between our considered systems. The advantage of the employed controller lies in the fact that it even works in the case of actuator or sensor failures, which may occur in many real-world situations. By introducing an improved Lyapunov–Krasovskii (L–K) functional and by using reciprocally convex technique, sufficient conditions are given in the form of linear matrix inequalities (LMIs) to ensure asymptotic stability of resulting synchronization error system. Numerical simulations of neural networks and Chua's circuit system are given to verify the effectiveness and less conservatism of the presented theoretical 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 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.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

A Global Synchronization Theorem for a Class of Chaotic Systems

1998 ◽  
Vol 08 (06) ◽  
pp. 1363-1369 ◽  
Author(s):  
Xiao Fan Wang ◽  
Zhi Quan Wang
Keyword(s):  
Chaotic Systems ◽  
Drive System ◽  
Chaotic Oscillator ◽  
Error Feedback ◽  
Global Synchronization ◽  
Lur’E Systems ◽  
State Variable ◽  
Chaotic Lur’E Systems ◽  
Driving Signal

This Letter proposes a new synchronization theorem for a subclass of chaotic Lur'e systems. We take a specific state variable of the drive system as the driving signal. We prove that globally synchronization can be attained via the simple linear error feedback. The approach is illustrated using Chua's chaotic oscillator and a hyperchaotic oscillator.

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

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