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.

ANALYSIS ON THE GLOBALLY EXPONENT SYNCHRONIZATION OF CHUA'S CIRCUIT USING ABSOLUTE STABILITY THEORY

2005 ◽  
Vol 15 (12) ◽  
pp. 3867-3881 ◽  
Author(s):  
XIAOXIN LIAO ◽  
PEI YU
Keyword(s):  
Control Systems ◽  
Stability Theory ◽  
Lyapunov Functions ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
Absolute Stability Theory

In this paper, the absolute stability theory and methodology for nonlinear control systems are employed to study the well-known Chua's circuit. New results are obtained for the globally exponent synchronization of two Chua's circuits. The explicit formulas can be easily applied in practice. With the aid of constructing Lyapunov functions, sufficient conditions are derived, under which two (drive-response) Chua's circuits are globally and exponentially synchronized, even if the motions of the systems are divergent to infinity. Numerical simulation results are given to illustrate the theoretical predictions.

Master-Slave Synchronization of Lur'e Systems

1997 ◽  
Vol 07 (03) ◽  
pp. 665-669 ◽  
Author(s):  
J. A. K. Suykens ◽  
J. Vandewalle
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
State Feedback ◽  
Lur’E Systems ◽  
Static State ◽  
Lur’E System ◽  
Feedback Matrix ◽  
Linear State ◽  
The One ◽  
Static State Feedback

In this paper we present a sufficient condition for master-slave synchronization of Lur'e systems. The scheme makes use of linear full static state feedback. The criterion is based on a Lur'e–Postnikov Lyapunov function for global asymptotic stability of the error system. The condition is basically the same as the one for global asymptotic stability of the Lur'e system, controlled with linear state feedback. The design of the feedback matrix is done by solving a constrained nonlinear optimization problem. The method is illustrated on the synchronization of Chua's circuit.

Nonregular Static State Feedback for Linear Bond Graph Models

2001 ◽  
Vol 34 (13) ◽  
pp. 71-76
Author(s):  
C. Sueur ◽  
A. Karim ◽  
G. Dauphin-Tanguy
Keyword(s):  
State Feedback ◽  
Bond Graph ◽  
Graph Models ◽  
Static State ◽  
Static State Feedback

scholarly journals Robust non-fragile LQ controllers: The static state feedback case

2000 ◽  
Vol 73 (2) ◽  
pp. 159-165 ◽  
Author(s):  
Domenico Famularo ◽  
Peter Dorato ◽  
Chaouki T. Abdallah ◽  
Wassim M. Haddad ◽  
Ali Jadbabaie
Keyword(s):  
State Feedback ◽  
Static State ◽  
Static State Feedback

Distributed Static State Feedback Control for DC Microgrids

2021 ◽  
pp. 306-314
Author(s):  
Sifeddine Benahmed ◽  
Pierre Riedinger ◽  
Serge Pierfederici
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Static State ◽  
Dc Microgrids ◽  
Static State Feedback
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