ANALYSIS ON THE GLOBALLY EXPONENT SYNCHRONIZATION OF CHUA'S CIRCUIT USING ABSOLUTE STABILITY THEORY

In this paper, the absolute stability theory and methodology for nonlinear control systems are employed to study the well-known Chua's circuit. New results are obtained for the globally exponent synchronization of two Chua's circuits. The explicit formulas can be easily applied in practice. With the aid of constructing Lyapunov functions, sufficient conditions are derived, under which two (drive-response) Chua's circuits are globally and exponentially synchronized, even if the motions of the systems are divergent to infinity. Numerical simulation results are given to illustrate the theoretical predictions.

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Absolute Stability Theory and Master-Slave Synchronization

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497001977 ◽

1997 ◽

Vol 07 (12) ◽

pp. 2891-2896 ◽

Cited By ~ 50

Author(s):

P. F. Curran ◽

J. A. K. Suykens ◽

L. O. Chua

Keyword(s):

Stability Theory ◽

Lyapunov Functions ◽

Absolute Stability ◽

State Feedback ◽

Lur’E Systems ◽

Static State ◽

Error System ◽

Static State Feedback ◽

Absolute Stability Theory

In this note we indicate the manner in which synchronization criteria may be developed for master-slave connected Lur'e systems. For flexibility we incorporate linear, static state feedback. The criteria presented are based on the generation of Lur'e–Postnikov type Lyapunov functions for the error system.

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CHAOTIC DYNAMICS AND SYNCHRONIZATION OF FRACTIONAL-ORDER CHUA'S CIRCUITS WITH A PIECEWISE-LINEAR NONLINEARITY

International Journal of Modern Physics B ◽

10.1142/s0217979205032115 ◽

2005 ◽

Vol 19 (20) ◽

pp. 3249-3259 ◽

Cited By ~ 32

Author(s):

JUN GUO LU

Keyword(s):

Lyapunov Exponent ◽

Fractional Order ◽

Stability Theory ◽

Chaos Synchronization ◽

Chaotic Dynamics ◽

Piecewise Linear ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Synchronization Method ◽

Simulation Results

In this paper, we numerically investigate the chaotic behaviors of the fractional-order Chua's circuit with a piecewise-linear nonlinearity. We find that chaos exists in the fractional-order Chua's circuit with order less than 3. The lowest order we find to have chaos is 2.7 in the homogeneous fractional-order Chua's circuit and 2.8 in the unhomogeneous fractional-order Chua's circuit. Our results are validated by the existence of a positive Lyapunov exponent. A chaos synchronization method is also presented for synchronizing the homogeneous fractional-order chaotic Chua's systems. The approach, based on stability theory of fractional-order linear systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

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CONTROLLING CHUA'S CIRCUIT

Journal of Circuits System and Computers ◽

10.1142/s0218126693000113 ◽

1993 ◽

Vol 03 (01) ◽

pp. 139-149 ◽

Cited By ~ 50

Author(s):

GUANRONG CHEN ◽

XIAONING DONG

Keyword(s):

Feedback Control ◽

Control Strategy ◽

Chaotic Systems ◽

Sufficient Conditions ◽

Control Process ◽

Periodic Signal ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Simulation Results ◽

Feedback Control Strategy

The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the well-known Chua's circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. Simple sufficient conditions for the controllability of this particular circuit are established. Simulation results are included to visualize the control process. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate periodic-signal generator to the original circuit.

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Inherent Stability of Multibody Systems with Variable-Stiffness Springs via Absolute Stability Theory

Complexity ◽

10.1155/2021/8662275 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Tianyang Hua ◽

Yinlong Hu

Keyword(s):

Time Domain ◽

Stability Theory ◽

Stability Problem ◽

Multibody Systems ◽

Absolute Stability ◽

Sufficient Conditions ◽

Variable Stiffness ◽

Circle Criterion ◽

Absolute Stability Theory ◽

Inherent Stability

In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur’e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems.

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SET STABILIZATION OF A MODIFIED CHUA'S CIRCUIT

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405012181 ◽

2005 ◽

Vol 15 (02) ◽

pp. 567-604 ◽

Cited By ~ 3

Author(s):

SHIHUA LI ◽

YU-PING TIAN

Keyword(s):

Equilibrium Point ◽

Lyapunov Stability ◽

Closed Loop ◽

Invariant Set ◽

Linear Feedback ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Linear Feedback Controller ◽

Simulation Results ◽

First Time

In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method.

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CONTROL OF n-SCROLL CHUA'S CIRCUIT

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409025134 ◽

2009 ◽

Vol 19 (11) ◽

pp. 3813-3822 ◽

Cited By ~ 16

Author(s):

ABDELKRIM BOUKABOU ◽

BILEL SAYOUD ◽

HAMZA BOUMAIZA ◽

NOURA MANSOURI

Keyword(s):

Numerical Simulations ◽

Fixed Points ◽

Periodic Orbits ◽

Predictive Control ◽

Control Method ◽

Sufficient Conditions ◽

Chua’S Circuit ◽

Unstable Periodic Orbits ◽

Chua's Circuit ◽

Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

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Controlling chaotic Chua's circuit based on piecewise quadratic Lyapunov functions method

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2004.02.056 ◽

2004 ◽

Vol 22 (5) ◽

pp. 1053-1061 ◽

Cited By ~ 12

Author(s):

Hongbin Zhang ◽

Chunguang Li ◽

Jian Zhang ◽

Xiaofeng Liao ◽

Juebang Yu

Keyword(s):

Lyapunov Functions ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Quadratic Lyapunov Functions ◽

Lyapunov Functions Method

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MAXIMUM DYNAMIC RANGE OF BIFURCATION OF CHUA'S CIRCUIT

Journal of Circuits System and Computers ◽

10.1142/s0218126693000289 ◽

1993 ◽

Vol 03 (02) ◽

pp. 471-481 ◽

Cited By ~ 2

Author(s):

A. A. A. NASSER ◽

E. E. HOSNY ◽

M. I. SOBHY

Keyword(s):

Linear Function ◽

Dynamic Range ◽

Piecewise Linear ◽

Piecewise Linear Function ◽

Bifurcation Parameter ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Simulation Results

This paper includes a method for detecting the maximum possible range of bifurcations based upon the multilevel oscillation technique. An application of the method to Chua's circuit, and new simulation results using the slope of the piecewise-linear function as a bifurcation parameter are presented.

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