| Asymptotic Controllability And Feedback Stabilization (1996) | |||||||||||||||
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| It is shown that every asymptotically controllable system can be stabilized by means of some (discontinuous) feedback law. One of the contributions of the paper is in defining precisely the meaning of stabilization when the feedback rule is not continuous. 1. Introduction A longstanding open question in nonlinear control theory concerns the relationship between asymptotic controllability to the origin in R n of a nonlinear system x = f(x; u) (1) by an "open loop" control u : [0; +1) ! U and the existence of a feedback control k : R n !Uwhich stabilizes trajectories of the system x = f(x; k(x)) (2) with respect to the origin. For the special case of linear control systems x = Ax + Bu, this relationship is well understood: asymptotic controllability is equivalent to the existence of a continuous (even linear) stabilizing feedback law. But it is well-known that continuous feedback laws may fail to exist even for simple asymptotically controllable nonlinear systems. This is espec... | |||||||||||||||
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