ON IMPULSIVE CONTROL AND ITS APPLICATION TO CHEN'S CHAOTIC SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1191-1197 ◽  
Author(s):  
ZHI-HONG GUAN ◽  
RUI-QUAN LIAO ◽  
FENG ZHOU ◽  
HUA O. WANG
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Asymptotical Stability ◽  
Impulsive Systems ◽  
Chaotic State ◽  
Chaos Suppression ◽  
Zero Equilibrium

In this paper, impulsive control of nonlinear systems and its application to Chen's chaotic system are considered. A new impulsive control method for chaos suppression, using Chen's system as an example, is developed. Some new general criteria for exponential stability and asymptotical stability of nonlinear impulsive systems are established and, particularly, some simple conditions sufficient for driving the chaotic state of Chen's system to its zero equilibrium are presented.

scholarly journals Lyapunov Control of Quantum Systems with Impulsive Control Fields

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wei Yang ◽  
Jitao Sun
Keyword(s):  
Lyapunov Functions ◽  
Control Method ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Quantum Systems ◽  
Impulsive Systems ◽  
Finite Dimensional ◽  
Lyapunov Control ◽  
Control Of Quantum Systems ◽  
Invariant Principle

We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.

A LIE ALGEBRAIC CONDITION OF STABILITY FOR HYBRID SYSTEMS AND APPLICATION TO HYBRID SYNCHRONIZATION

2009 ◽  
Vol 19 (01) ◽  
pp. 379-386 ◽  
Author(s):  
SHOUWEI ZHAO ◽  
JITAO SUN
Keyword(s):  
Exponential Stability ◽  
Lie Algebra ◽  
Global Exponential Stability ◽  
Impulsive Control ◽  
Impulsive Systems ◽  
Algebraic Condition ◽  
System Synchronization ◽  
Hybrid Synchronization ◽  
New Criterion ◽  
Existing Result

In this paper, we first present a Lie algebraic condition for global exponential stability of linear switched and impulsive systems. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Hurwitz/Schur stable we derive a new criterion for global exponential stability of linear switched and impulsive systems. Then a simple sufficient condition in terms of Lie algebra is established for a nonlinear system synchronization using a hybrid switched and impulsive control. As an application, Chua's chaotic circuit's synchronization is investigated by our method while synchronization cannot be achieved with the existing result.

scholarly journals Exponential stability analysis of nonlinear systems with bounded gain error

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xingkai Hu ◽  
Linru Nie
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Impulsive Control ◽  
Practical Application ◽  
Chua’S Oscillator ◽  
Gain Error ◽  
Switched Control

AbstractConsidering technology limitation or device restriction in practical application, we formulate new nonlinear systems with bounded gain error, which contain switched control and impulsive control. We then investigate the exponential stability of the considered systems. Finally, the effectiveness of the proposed criteria is confirmed via an example based on Chua’s oscillator.

Ferroelectric Systems with Controlled Chaos

1997 ◽  
Vol 07 (01) ◽  
pp. 199-204 ◽  
Author(s):  
R. Habel ◽  
H. Beige
Keyword(s):  
Nonlinear Systems ◽  
Chaotic System ◽  
Electronic Device ◽  
Period Doubling ◽  
Frequency Range ◽  
Chaotic State ◽  
Ferroelectric Crystal ◽  
Nonlinear Capacitance ◽  
Resonance Circuit ◽  
Series Resonance

A practically implemented control of a chaotic system in the frequency range of 1…20 kHz is described. We use a ferroelectric crystal as a nonlinear capacitance in a series resonance circuit. So the circuit shows all features of nonlinear systems like period doubling, chaos or periodic windows. The required control of the chaotic state can be carried out as fast as necessary by using an analogous electronic device.

Coexisting attractors, circuit realization and impulsive synchronization of a new four-dimensional chaotic system

2019 ◽  
Vol 33 (03) ◽  
pp. 1950026 ◽  
Author(s):  
Chengqun Zhou ◽  
Chunhua Yang ◽  
Degang Xu ◽  
Chaoyang Chen
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Period Doubling ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Impulsive Synchronization ◽  
Periodic Attractors ◽  
Different Types ◽  
Two Equilibria

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example.

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