CHAOTIFICATION OF LINEAR CONTINUOUS-TIME SYSTEMS USING SIMPLE NONLINEAR FEEDBACK

2003 ◽  
Vol 13 (10) ◽  
pp. 3099-3106 ◽  
Author(s):  
WALLACE K. S. TANG ◽  
G. Q. ZHONG
Keyword(s):  
Continuous Time ◽  
Chaotic Dynamics ◽  
Feedback Controller ◽  
Numerical Continuation ◽  
Nonlinear Feedback ◽  
Third Order ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Simple Feedback ◽  
Nonlinear State

A nonlinear state feedback controller is proposed for the generation of chaos in third-order linear autonomous continuous time systems. With a simple feedback controller of the form g(x)=βx|x|, chaotic dynamics can be observed. Bifurcation analysis and the verification of the existence of chaos are given based on numerical continuation techniques and the Shil'nikov theorem. Both computer simulation and circuit implementation demonstrate the chaotification effect of this simple feedback controller.

scholarly journals Positivity and Linearization of a Class of Nonlinear Continuous–Time Systems by State Feedbacks

2015 ◽  
Vol 25 (4) ◽  
pp. 827-831 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Nonlinear State ◽  
Continuous Time System

Abstract The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.

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