A new method for stabilizing unstable periodic orbits of continuous-time systems. Application to control of chaos

2012 ◽  
Author(s):  
Thiago P. Chagas ◽  
Pierre-Alexandre Bliman ◽  
Karl H. Kienitz
Keyword(s):  
Periodic Orbits ◽  
Continuous Time ◽  
New Method ◽  
Unstable Periodic Orbits ◽  
Control Of Chaos ◽  
Continuous Time Systems ◽  
Time Systems

scholarly journals Computation of positive realizations for descriptor linear continuous-time systems

2018 ◽  
Vol 19 (12) ◽  
pp. 428-432
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Transfer Matrices ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

DELAYED FEEDBACK CONTROL WITH STATE PREDICTOR FOR CONTINUOUS-TIME CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (05) ◽  
pp. 1067-1077 ◽  
Author(s):  
HIROYUKI NAKAJIMA
Keyword(s):  
Feedback Control ◽  
Continuous Time ◽  
Equilibrium Points ◽  
Autonomous Systems ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Sufficient Condition ◽  
Unstable Periodic Orbits ◽  
Continuous Time Systems ◽  
Time Systems

We propose an application of state predictor to delayed feedback control (DFC) for continuous-time dynamical systems. First, we define the DFC for continuous-time systems clearly. Next, on the basis of this definition, we propose a DFC method with state-predictor to stabilize unstable equilibrium points in autonomous systems and derive a sufficient condition for stabilization. Then we extend this method to stabilizing unstable periodic orbits and also derive a sufficient condition for stabilization. Finally, we briefly discuss the relation between the conditions for stabilization of our methods and those of the dynamic DFC and the prediction-based feedback control for discrete-time systems.

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