Nonlinear H∞ Synchronization of Chaotic Lur'e Systems

In this paper a master-slave synchronization scheme for Lur'e systems is investigated, which consists of vector field modulation by means of the message signal. Using a full state error feedback mechanism and formulating the synchronization problem within the standard plant framework of modern control theory, it is shown how the original message can be recovered for a class of binary-valued continuous time reference inputs or message signals. Input/output properties of the synchronization scheme are analyzed using the system-theoretical approach of dissipativity with a quadratic storage function and a supply rate of finite L2-gain. The feedback matrix is designed such that the influence of the exogenous input on a tracking error is minimized, corresponding to a so-called nonlinear H∞ synchronization scheme. Channel noise is taken into account in the design. The method is illustrated on Chua's circuit and an n-double scroll circuit.

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ROBUST SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016914 ◽

2006 ◽

Vol 16 (11) ◽

pp. 3421-3433 ◽

Cited By ~ 13

Author(s):

XIAOFENG WU ◽

MUHONG WANG

Keyword(s):

Frequency Domain ◽

Error Bound ◽

Sufficient Conditions ◽

Synchronization Error ◽

Linear Matrix ◽

Lur’E Systems ◽

Parameter Mismatch ◽

Chaotic Lur’E Systems ◽

Definition Of ◽

Synchronization Scheme

The sufficient conditions for chaos synchronization of two nonidentical systems by replacing variables control have not been proposed until now. In this paper, synchronization of two chaotic Lur'e systems with parameter mismatch by replacing variables control is studied. First of all, we present a master-slave Lur'e systems synchronization scheme with both parameter mismatch and replacing variables control, and derive a responsive error system for the scheme. A new definition of synchronization with finite L 2-gain is then introduced. Based on the definition, the sufficient synchronization criteria which are in the form of linear matrix inequality (LMI) are proved using a quadratic Lyapunov function. By means of MKY lemma the frequency domain criteria are further derived from the obtained LMIs. These frequency domain criteria are illustrated on the master-slave Chua's circuits with parameter mismatch so that the ranges of the parameters of Chua's circuit are analytically solved in the sense of the synchronization with finite L 2-gain by replacing singe-variable control. The illustrative examples verify that within the ranges of the parameters it is possible to synchronize the master-slave Chua's circuits up to a small synchronization error bound, even the qualitative behaviors of the slave circuit are different from that of the master one, such as the trajectory of the master circuit is chaotic and that of the slave divergent. The relation between the synchronization error bound and parameter mismatch is shown.

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Global Lagged Finite-Time Synchronization of Two Chaotic Lur’e Systems Subject to Time Delay

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127415501618 ◽

2015 ◽

Vol 25 (12) ◽

pp. 1550161 ◽

Cited By ~ 2

Author(s):

Yun Chen ◽

Xiaofeng Wu ◽

Qian Lin

Keyword(s):

Time Delay ◽

Finite Time ◽

Time Synchronization ◽

Signal Transmission ◽

Feedback Controller ◽

Linear Matrix ◽

Lur’E Systems ◽

Chaotic Lur’E Systems ◽

Variable Substitution ◽

Synchronization Scheme

This paper investigates the global lagged finite-time synchronization of the master-slave Lur’e systems subject to time delay of signal transmission. By designing a variable-substitution and feedback controller, a master-slave finite-time synchronization scheme for the Lur’e systems with time delay is built up. Two delay-independent global lagged finite-time synchronization criteria are proved in the forms of linear matrix inequalities (LMIs), and the corresponding settling time of synchronization is analytically estimated. The obtained LMI criteria are applied to Chua’s oscillators, obtaining some easily implemented algebraic criteria under various single-variable-substitution and feedback controller, which are then optimized to improve their conservative property. Finally, several numerical examples are illustrated to verify the effectiveness of the optimized criteria.

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MASTER–SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS WITH TIME-DELAY

International Journal of Bifurcation and Chaos ◽

10.1142/s021812740100295x ◽

2001 ◽

Vol 11 (06) ◽

pp. 1707-1722 ◽

Cited By ~ 182

Author(s):

M. E. YALÇIN ◽

J. A. K. SUYKENS ◽

J. VANDEWALLE

Keyword(s):

Time Delay ◽

Optimization Problem ◽

Sufficient Conditions ◽

Matrix Inequality ◽

Lur’E Systems ◽

Delay Effects ◽

Feedback Matrix ◽

Error System ◽

Delay Dependent ◽

Synchronization Scheme

In this paper time-delay effects on the master–slave synchronization scheme are investigated. Sufficient conditions for master–slave synchronization of Lur'e systems are presented for a known time-delay in the master and slave systems. A delay-dependent synchronization criterion is given based upon a new Lyapunov–Krasovskii function. The derived criterion is a sufficient condition for global asymptotic stability of the error system, expressed by means of a matrix inequality. The feedback matrix follows from solving a nonlinear optimization problem. The method is illustrated for the synchronization of Chua's circuits, 5-scroll attractors and hyperchaotic attractors.

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A Global Synchronization Theorem for a Class of Chaotic Systems

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001066 ◽

1998 ◽

Vol 08 (06) ◽

pp. 1363-1369 ◽

Cited By ~ 5

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.

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DELAY-DEPENDENT SYNCHRONIZATION CRITERION FOR LUR'E SYSTEMS WITH DELAY FEEDBACK CONTROL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016677 ◽

2006 ◽

Vol 16 (10) ◽

pp. 3087-3091 ◽

Cited By ~ 40

Author(s):

YONG HE ◽

GUILIN WEN ◽

QING-GUO WANG

Keyword(s):

Time Delay ◽

Delay Systems ◽

Matrix Approach ◽

Time Delay Systems ◽

Stability Studies ◽

Lur’E Systems ◽

Weighting Matrix ◽

Delay Feedback Control ◽

Delay Dependent ◽

Synchronization Scheme

A master-slave synchronization scheme for Lur'e systems is studied for a known delay existing between master and slave systems. Based on the latest development of stability studies for time-delay systems, a new delay-dependent synchronization criterion is derived by the free-weighting matrix approach. The criterion shown by example is less conservative than the existing synchronization criteria.

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