Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay

2008 ◽  
Vol 55 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Jianquan Lu ◽  
Jinde Cao ◽  
D.W.C. Ho
Keyword(s):  
Time Varying ◽  
Adaptive Stabilization ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Chaotic Lur’E Systems ◽  
Varying Delay

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

FURTHER RESULTS ON MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY

2008 ◽  
Vol 18 (01) ◽  
pp. 187-202 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TÔRRES
Keyword(s):  
Communication Systems ◽  
Functional Differential Equations ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Feedback Control ◽  
Functional Differential ◽  
Varying Delay

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

MASTER-SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS BASED ON TIME-VARYING DELAY FEEDBACK CONTROL

2007 ◽  
Vol 17 (11) ◽  
pp. 4159-4166 ◽  
Author(s):  
HE HUANG ◽  
JINDE CAO
Keyword(s):  
Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Master System ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the master-slave synchronization problem of Lur'e systems based on time-varying delay feedback control. The time-varying delay is only assumed to be bounded. Delay-dependent conditions are derived such that the controlled slave system can track the master system. The synchronization criteria are expressed in terms of linear matrix inequality, which can be checked readily by using some standard numerical packages. A simulation example is provided to demonstrate the effectiveness of the proposed approach.

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