H∞ SYNCHRONIZATION OF SWITCHED CHAOTIC SYSTEMS AND ITS APPLICATION TO SECURE COMMUNICATIONS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250058 ◽  
Author(s):  
ZHANG-LIN WAN ◽  
TEH-LU LIAO ◽  
YI-YOU HOU ◽  
JUN-JUH YAN
Keyword(s):  
Communication Systems ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Secure Communications ◽  
Switching Law ◽  
Synchronization Problem ◽  
Matrix Equality ◽  
Security Communication

This paper deals with the H∞ synchronization problem of switched chaotic systems accompanied by a time-driven switching law and its application to secure communications. Based on the Lyapunov stability theory and linear matrix inequality (LMI) and linear matrix equality (LME) optimization techniques, an output feedback controller that guarantees the synchronization of switched master-slave chaotic systems is designed. A chaotic encryption technique that uses synchronization is proposed for securely transmitting a message over public channels. Numerical simulations of both analog and digital security communication systems are conducted to demonstrate the effectiveness of the proposed methods.

scholarly journals A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm

2015 ◽  
Vol 5 (1) ◽  
pp. 739-747 ◽  
Author(s):  
I. Ahmad ◽  
A. Saaban ◽  
A. Ibrahin ◽  
M. Shahzad
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Control Techniques ◽  
Synchronization Problem ◽  
Response Systems ◽  
Globally Stable ◽  
Time Evaluation

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.

Synchronization Controlling for a Permanent Magnet Synchronous Motor via Linear Feedback with Single State

2012 ◽  
Vol 442 ◽  
pp. 472-476 ◽  
Author(s):  
Ji Gui Jian ◽  
Zhi Hua Zhao ◽  
Wei Wei Wang
Keyword(s):  
Permanent Magnet ◽  
Chaotic Systems ◽  
Permanent Magnet Synchronous Motor ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Synchronous Motor ◽  
Exponential Synchronization ◽  
Linear Feedback ◽  
Control Approach ◽  
Synchronization Problem

This paper treats the globally exponential synchronization problem of the permanent magnet synchronous motor chaotic system. Based on Lyapunov stability theory and some inequalities techniques, one novel control approach, namely linear feedback control with one state is proposed to realize the globally exponential synchronization of two permanent magnet synchronous motor chaotic systems. In this case, some sufficient conditions for the globally exponential synchronization of two chaotic systems are obtained analytically. The controllers here designed have simple structure and less conservation. The numerical simulation results show the effectiveness of the method.

IMPULSIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA LINEAR MATRIX INEQUALITIES

2006 ◽  
Vol 16 (01) ◽  
pp. 221-227 ◽  
Author(s):  
Y. JI ◽  
C. Y. WEN ◽  
Z. G. LI
Keyword(s):  
Linear Matrix Inequalities ◽  
Chaotic Systems ◽  
Structural Knowledge ◽  
Linear Matrix ◽  
Secure Communications ◽  
Bandwidth Efficiency ◽  
Matrix Inequalities ◽  
Impulsive Synchronization

Impulsive synchronization of chaotic systems is studied in this paper. By exploring the structural knowledge of the systems and using linear matrix inequalities, some less conservative conditions than existing results are derived. With the new conditions, the bound of intervals for transmitting impulses can be increased and this results in higher bandwidth efficiency. Our results are thus able to improve the efficiencies of the existing technologies on chaotic secure communications and chaotic spread communications.

SYNCHRONIZATION THEOREM FOR A CHAOTIC SYSTEM

1995 ◽  
Vol 05 (01) ◽  
pp. 297-302 ◽  
Author(s):  
JÖRG SCHWEIZER ◽  
MICHAEL PETER KENNEDY ◽  
MARTIN HASLER ◽  
HERVÉ DEDIEU
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Secure Communications ◽  
Error Feedback ◽  
Response System ◽  
Synchronization Method

Since Pecora & Carroll [Pecora & Carroll, 1991; Carroll & Pecora, 1991] have shown that it is possible to synchronize chaotic systems by means of a drive-response partition of the systems, various authors have proposed synchronization schemes and possible secure communications applications [Dedieu et al., 1993, Oppenheim et al., 1992]. In most cases synchronization is proven by numerically computing the conditional Lyapunov exponents of the response system. In this work a new synchronization method using error-feedback is developed, where synchronization is provable using a global Lyapunov function. Furthermore, it is shown how this scheme can be applied to secure communication systems.

Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

2017 ◽  
Vol 40 (10) ◽  
pp. 3078-3087 ◽  
Author(s):  
Xiaona Song ◽  
Shuai Song ◽  
Bo Li ◽  
Ines Tejado Balsera
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Hybrid Control ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Secure Communications ◽  
Uncertain Parameters ◽  
Matrix Inequalities

In this paper, the adaptive projective synchronization of time-delayed fractional-order neural networks is considered. Using the active control and adaptive control methods, efficient hybrid control strategies are designed for time-delayed fractional-order neural networks with uncertain parameters. Based on a new version of fractional-order Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities, which is easily checked and applied to practical systems. Finally, numerical simulations and application of the proposed methods to secure communications have been presented to validate the synchronization method.

DIGITAL CRYPTOGRAPHY AND FEEDBACK SYNCHRONIZATION OF CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (04) ◽  
pp. 521-529 ◽  
Author(s):  
MALA MITRA ◽  
SANTO BANERJEE
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Coupled System ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Feedback Controller ◽  
New Method ◽  
Secure Communications

Secure communications via chaotic synchronization is demonstrated in this literature. At first we have designed a feedback controller for chaotic synchronization utilizing the Lyapunov stability theory for cascade-connected systems.The method has been applied successfully to make two identical systems globally asymptotically synchronized. The result of numerical simulations are given to validate the effectiveness of this method. Then we have discussed a new method of cryptography for this coupled system which is very simple to implement and effective.

Disturbed Chaotic Systems Synchronization via Robust Mixed Functional Projective Method

2014 ◽  
Vol 496-500 ◽  
pp. 1293-1297
Author(s):  
Tao Fan ◽  
Ning Fang ◽  
Fei Tan
Keyword(s):  
State Feedback ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Generalized Synchronization ◽  
Linear State ◽  
Control And Synchronization

Robust mixed functional projective synchronization (RMFPS), which is the generalized synchronization idea developed very recently, is investigated in this paper. Based on Lyapunov stability theory and linear matrix inequality (LMI), some novel stability criterions for the synchronization between drive and response chaotic systems with disturbances are derived, and then a simple linear state feedback synchronization controller is designed. In order to test the proposed method, numerical simulations of hyper-chaotic unified systems with disturbances are then provided to show the effectiveness and feasibility of this chaos control and synchronization schemes.

FUZZY MODEL-BASED APPROACH TO CHAOTIC ENCRYPTION USING SYNCHRONIZATION

2003 ◽  
Vol 13 (01) ◽  
pp. 215-225 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
PETER LIU ◽  
CHIAN-SONG CHIU ◽  
TUNG-SHENG CHIANG
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Chaotic Encryption ◽  
Communication Structure ◽  
Model Based ◽  
Synchronization Problem ◽  
Chaotic Signals ◽  
Selection Of

This paper proposes a fuzzy model-based chaotic encryption approach using synchronization. The cryptosystem uses T–S fuzzy models to exactly represent discrete-time chaotic systems into separate linear systems. Then the synchronization problem is solved using linear matrix inequalities. The advantages of this approach are: the general and systematic T–S fuzzy model design methodology suitable for well-known Luré type discrete-time chaotic systems; flexibility in selection of chaotic signals for cryptosystem secure key generator; and multiuser capabilities. Especially taking a chaotic superincreasing sequence as an encryption key enhances the chaotic communication structure to a higher-level of security compared to traditional masking methods. In addition, numerical simulations and DSP-based experiments are carried out to verify the validity of theoretical results.

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 Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Muhammad Majid Hussain ◽  
Muhammad Siddique ◽  
Ziyad M. Almohaimeed ◽  
Romaisa Shamshad ◽  
Rizwan Akram ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Inequality Constraints ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Synchronization Errors ◽  
Nonlinear Properties ◽  
State Approximation ◽  
Approximation Errors ◽  
The Difference ◽  
Neuronal Systems

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and nonadaptive laws for control systems, and nonlinear properties, the intermingling conditions for state approximation errors and approximated synchronization errors are established as nonlinear matrix inequalities. A solution to the resulting inequality constraints using a two-step linear matrix inequality (LMI)-based approach is introduced, giving essential and adequate conditions to extract values from the controller gain and observer gain matrices. Simulation of the suggested synchronization procedure for FitzHugh–Nagumo neuronal systems is demonstrated to expand the viability of the suggested observer-based control techniques.

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