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Clocks and insensitivity to small measurement errors. (English) Zbl 0984.93068

The paper considers the nonlinear control system \[ \dot x= f(x,u) \] with a stabilizing feedback of the form \(u= k(x)\). It is required that this feedback should be stabilizing if \(k(x)\) is replaced by \(k(x+ e)\) where \(e\) is small in some sense. Since in definite cases only discontinuous feedback is stabilizing, one considers piecewise constant feedback. A Lyapunov function based analysis gives some rules for choosing the sampling points for the feedback (the sampling schedule, as called by the author). The results are obtained for the case of global stabilization. Then non-global stability and systems on manifolds are considered.

MSC:

93D15 Stabilization of systems by feedback
93B52 Feedback control
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References:

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