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IMA Journal of Mathematical Control and Information 2003 20(1):37-64; doi:10.1093/imamci/20.1.37
© 2003 by Institute of Mathematics and its Applications
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Necessary and sufficient conditions for the existence of stabilizing feedback for control systems

Iasson Karafyllis1

1 Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

We prove that the existence of a non-smooth control Lyapunov function is a necessary and sufficient condition for the existence of an ordinary smooth time-varying feedback that stabilizes an affine time-varying control system. Results concerning the non-affine case are also provided.

Keywords: time-varying feedback; affine control systems; global stabilization; Lyapunov functions.


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