Title :
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
fDate :
10/1/1997 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
