Asymptotic controllability implies feedback stabilization

Author

Clarke, Francis H. ; Ledyaev, Yuri S. ; Sontag, Eduardo D. ; Subbotin, Andrei I.

Author_Institution

Lyon I Univ., Villeurbanne, France

Volume

42

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

1394

Lastpage

1407

Abstract

It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a control-Lyapunov function, iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium. A major technical problem, and one of the contributions of the present paper, concerns the precise meaning of “solution” when using a discontinuous controller

Keywords

Lyapunov methods; asymptotic stability; controllability; feedback; nonlinear control systems; robust control; sampled data systems; asymptotic controllability; control-Lyapunov function; discontinuous controller; discontinuous feedback law; feedback stabilization; global stabilization; pointwise optimization; Control systems; Controllability; Councils; Feedback control; Linear feedback control systems; Mathematics; Negative feedback; Nonlinear control systems; Nonlinear systems; Time varying systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.633828

Filename

633828