Piecewise quadratic common Lyapunov functions and the absolute stability of single variable Lur'e systems

2004 ◽  
Author(s):  
R. Duignan
Keyword(s):  
Lyapunov Functions ◽  
Absolute Stability ◽  
Single Variable ◽  
Lur’E Systems ◽  
The Absolute ◽  
Common Lyapunov Functions

Absolute Stability Theory and Master-Slave Synchronization

1997 ◽  
Vol 07 (12) ◽  
pp. 2891-2896 ◽  
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.

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

2005 ◽  
Vol 15 (02) ◽  
pp. 617-635 ◽  
Author(s):  
XIAOFENG WU ◽  
YI ZHAO ◽  
SHENG ZHOU
Keyword(s):  
Absolute Stability ◽  
Sufficient Conditions ◽  
Single Variable ◽  
Optimization Scheme ◽  
Lag Synchronization ◽  
Lur’E Systems ◽  
Variable Control ◽  
Chaotic Lur’E Systems ◽  
Parameter Ranges ◽  
Absolute Stability Theory

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results.

The Problem of Absolute Stability of a Class of Lurie Switched Time-Delay Systems

2012 ◽  
Vol 433-440 ◽  
pp. 2641-2644
Author(s):  
Bei Xing Mao ◽  
Dong Xiao Wang
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Stability Problem ◽  
Time Delays ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Absolute ◽  
Absolute Stability Problem

The absolute stability problem of Lurie time-delays switched systems is investigated. All the subsystems are Lurie systems. Lyapunov functions is used to derive the sufficient conditions for the absolute stability of systems

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