Switched Systems, Lur’e Systems, Absolute Stability, Aizerman Problem

2019 ◽  
Vol 80 (8) ◽  
pp. 1375-1389 ◽  
Author(s):  
V. A. Kamenetskiy
Keyword(s):  
Switched Systems ◽  
Absolute Stability ◽  
Lur’E Systems ◽  
Aizerman Problem

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.

scholarly journals Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xian Liu ◽  
Jiajia Du ◽  
Qing Gao
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Time Domain ◽  
Absolute Stability ◽  
Lyapunov Method ◽  
Lur’E Systems ◽  
Kyp Lemma

The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

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.

Parametric absolute stability of Lur'e systems

1998 ◽  
Vol 43 (11) ◽  
pp. 1649-1653 ◽  
Author(s):  
T. Wada ◽  
M. Ikeda ◽  
Y. Ohta ◽  
D.D. Siljak
Keyword(s):  
Absolute Stability ◽  
Lur’E Systems
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