Stabilization of three-dimensional chaotic systems via single state feedback controller

2010 ◽  
Vol 374 (13-14) ◽  
pp. 1488-1492 ◽  
Author(s):  
Wenguang Yu
Keyword(s):  
State Feedback ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Single State

Synchronization of a Class of Chaotic and Hyperchaotic Systems via a Simple Universal Control Method

2012 ◽  
Vol 184-185 ◽  
pp. 798-801
Author(s):  
Zhi Liu ◽  
Ming Ju Hao
Keyword(s):  
Chaos Synchronization ◽  
State Feedback ◽  
Chaotic Systems ◽  
Control Method ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Universal Method ◽  
Error System ◽  
Single State ◽  
Hyperchaotic Systems

This paper investigates the synchronization of chaotic and hyperchaotic systems, and proposes a simple and universal method for chaos synchronization through investigating the dynamical behavior of the chaotic error system. In comparison with previous methods, the present controllers are simpler than the existing results. Especially, for some class of three dimensional chaotic systems, the obtained controllers in this paper contain single state feedback. Numerical simulations verify the effectiveness and correctness of the proposed method.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

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