scholarly journals Inherent Stability of Multibody Systems with Variable-Stiffness Springs via Absolute Stability Theory

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tianyang Hua ◽  
Yinlong Hu
Keyword(s):  
Time Domain ◽  
Stability Theory ◽  
Stability Problem ◽  
Multibody Systems ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Variable Stiffness ◽  
Circle Criterion ◽  
Absolute Stability Theory ◽  
Inherent Stability

In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur’e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems.

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.

Extensions of mixed-µbounds to monotonic and odd monotonic nonlinearities using absolute stability theory

1994 ◽  
Vol 60 (5) ◽  
pp. 905-951 ◽  
Author(s):  
WASSIM M. HADDAD ◽  
JONATHAN P. HOW ◽  
STEVEN R. HALL ◽  
DENNIS S. BERNSTEIN
Keyword(s):  
Stability Theory ◽  
Absolute Stability ◽  
Absolute Stability Theory

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.

LAG SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

2005 ◽  
Vol 15 (02) ◽  
pp. 617-635 ◽  
Author(s):  
XIAOFENG WU ◽  
YI ZHAO ◽  
SHENG ZHOU
Keyword(s):  
Absolute Stability ◽  
Sufficient Conditions ◽  
Single Variable ◽  
Optimization Scheme ◽  
Lag Synchronization ◽  
Lur’E Systems ◽  
Variable Control ◽  
Chaotic Lur’E Systems ◽  
Parameter Ranges ◽  
Absolute Stability Theory

In this paper, we propose a method to research lag synchronization of the identical master-slave chaotic Lur'e systems via replacing variables control with time delay. By means of absolute stability theory, we prove two types of sufficient conditions for the lag synchronization: Lur'e criterion and frequency domain criterion. Based on the criteria, we suggest an optimization scheme to design the control variables. Applying the scheme to general Chua's circuits, we obtain the parameter ranges in which the master-slave Chua's circuits laggingly synchronize or not by varied single-variable control. Finally, we cite the examples by illustration of the results.

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