Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearities

2007 ◽  
Vol 17 (9) ◽  
pp. 829-841 ◽  
Author(s):  
Chunyu Yang ◽  
Qingling Zhang ◽  
Linna Zhou
Keyword(s):  
Lyapunov Functions ◽  
Absolute Stability ◽  
Stability Criteria ◽  
Lur’E Systems

scholarly journals Novel Delay-Decomposing Approaches to Absolute Stability Criteria for Neutral-Type Lur’e Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Liang-Dong Guo ◽  
Sheng-Juan Huang ◽  
Li-Bing Wu
Keyword(s):  
Absolute Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Lur’E Systems ◽  
Delay Dependent ◽  
Numerical Complexity ◽  
Variation Interval

The problem of absolute stability analysis for neutral-type Lur’e systems with time-varying delays is investigated. Novel delay-decomposing approaches are proposed to divide the variation interval of the delay into three unequal subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on the obtained subintervals. The integral inequality method and the reciprocally convex technique are utilized to deal with the derivative of the LKFs. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). Compared with some previous criteria, the proposed ones give the results with less conservatism and lower numerical complexity. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.

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.

Robust absolute stability criteria for uncertain Lur'e systems of neutral type

2007 ◽  
Vol 18 (3) ◽  
pp. 278-295 ◽  
Author(s):  
Qing-Long Han ◽  
Anke Xue ◽  
Shirong Liu ◽  
Xinghuo Yu
Keyword(s):  
Absolute Stability ◽  
Neutral Type ◽  
Stability Criteria ◽  
Lur’E Systems
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