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IMA Journal of Mathematical Control and Information 2003 20(4):441-446; doi:10.1093/imamci/20.4.441
© 2003 by Institute of Mathematics and its Applications
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Creating new stable periodic orbit by small region feedback control

Xiao-Song Yang1

1 Centre for Systems and Control and Department of Automation, Xiamen University, Xiamen, Fujian 361005, China

In this paper an important problem in chaos control theory concerning the possibility of generating a new stable periodic solution by a small feedback control law for a dynamical system is addressed. It is proved that a solution with an initial point being some kind of non-wandering property can become a new asymptotically stable solution by a small feedback control law. This shows that the popular opinion that a small control law is not able to create a new periodic point is untrue, and suggests a new approach to controlling chaos.

Keywords: chaotic systems; non-wandering point; small control law.


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