A New Approach to Absolute Stability for Lur'e Systems with Time-Varying Delay

2010 ◽  
Author(s):  
Huimin Zhao ◽  
Zhiqiang Zuo
Keyword(s):  
Absolute Stability ◽  
Time Varying ◽  
Lur’E Systems ◽  
New Approach ◽  
Time Varying Delay ◽  
Varying Delay

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.

scholarly journals New Absolute Stability Conditions of Lur’e Systems with Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wang ◽  
Hong-Bing Zeng
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
The Relationship ◽  
Varying Delay

This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.

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.

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