ESTIMATION OF AN ATTRACTION REGION IN ONE-DIMENSIONAL DELAYED-FEEDBACK CONTROL SYSTEMS

2005 ◽  
Vol 15 (02) ◽  
pp. 689-695
Author(s):  
KEIJI KONISHI
Keyword(s):  
Control Systems ◽  
Chaotic Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
One Dimensional ◽  
Feedback Control Systems ◽  
Linear Matrix Inequality Approach ◽  
Feedback Method

This paper presents a simple numerical scheme for estimating the attraction region of a fixed point in one-dimensional discrete-time chaotic systems controlled by the delayed-feedback method. This scheme employs the well-known linear matrix inequality approach. A systematic procedure for estimating the region is provided, and numerical examples are used to validate the results.

T–S FUZZY ADAPTIVE DELAYED FEEDBACK SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3253-3267 ◽  
Author(s):  
CHOON KI AHN ◽  
PYUNG SOO KIM
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Fuzzy Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Takagi Sugeno ◽  
Fuzzy Adaptive

In this paper, we propose a new adaptive synchronization method, called a fuzzy adaptive delayed feedback synchronization (FADFS) method, for time-delayed chaotic systems with uncertain parameters. An FADFS controller that is based on the Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model, and delayed feedback control is developed to guarantee adaptive synchronization. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example using a time-delayed Lorenz system is discussed to assess the validity of the proposed FADFS method.

MASTER-SLAVE SYNCHRONIZATION OF NONAUTONOMOUS CHAOTIC SYSTEMS AND ITS APPLICATION TO ROTATING PENDULUMS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250147 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Phase Locked Loops ◽  
Linear Matrix ◽  
Delayed Feedback Controller ◽  
Delay Dependent ◽  
Time Delayed Feedback

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

DELAYED FEEDBACK $\mathcal{H}_{\infty}$ SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS BASED ON T–S FUZZY MODEL

2010 ◽  
Vol 24 (02) ◽  
pp. 211-224 ◽  
Author(s):  
CHOON KI AHN ◽  
JUNG HUN PARK
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
External Disturbance ◽  
Fuzzy Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Linear Matrix ◽  
Control Scheme ◽  
Norm Constraint ◽  
New Formula

In this letter, we propose a new [Formula: see text] synchronization method, called a delayed feedback fuzzy [Formula: see text] synchronization (DFFHS) method, for time-delayed chaotic systems with external disturbance. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the DFFHS controller is presented to not only guarantee aymptotical synchronization but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed DFFHS method.

BIFURCATION DYNAMICS IN CONTROL SYSTEMS

1999 ◽  
Vol 09 (01) ◽  
pp. 287-293 ◽  
Author(s):  
GUANRONG CHEN ◽  
JIALIANG LU ◽  
BRENT NICHOLAS ◽  
SWATIPRAKASH M. RANGANATHAN
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Main Concern ◽  
Feedback Strategy ◽  
Feedback Control Systems ◽  
Time Delayed Feedback ◽  
Control Purpose

This paper is to report the observation that when the popular time-delayed feedback strategy is used for control purpose, it may actually create unwanted bifurcations. Hopf bifurcation created by delayed feedback control is the main concern of this article, but some other types of bifurcations are also observed to exist in such delayed-feedback control systems. The observations are illustrated by computer simulations.

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