Geodesic
The method of normal local stabilization
Problemy analiza, Tome 8 (2019) no. 1, pp. 72-83.

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A problem of nonlinear systems stabilization is studied. Admissible controls are piecewise constant. The notion of normal local stabilizability is proposed. A point $P$ (not necessary equilibrium) is normally locally stabilizable if for any $\tau>0$ there exists such neighborhood $D(P;\tau)$ of $P$ that any point $x \in D(P;\tau)$ can be steered, in a time less than $\tau$, to any neighborhood of $P$ and remains there. The constructive method of normal local stabilization of nonlinear autonomous systems is presented. This method involves a special sequence of contracting cylinders containing a trajectory. A domain of attraction of a given point is constructed.
Keywords: dynamical system, positive basis, normal stabilization. 
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A. N. Kirillov. The method of normal local stabilization. Problemy analiza, Tome 8 (2019) no. 1, pp. 72-83. http://geodesic.mathdoc.fr/item/PA_2019_8_1_a5/

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