Geodesic
The method of normal local stabilization
Problemy analiza, Tome 8 (2019) no. 1, pp. 72-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{PA_2019_8_1_a5,
     author = {A. N. Kirillov},
     title = {The method of normal local stabilization},
     journal = {Problemy analiza},
     pages = {72--83},
     year = {2019},
     volume = {8},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_1_a5/}
}
TY  - JOUR
AU  - A. N. Kirillov
TI  - The method of normal local stabilization
JO  - Problemy analiza
PY  - 2019
SP  - 72
EP  - 83
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_1_a5/
LA  - en
ID  - PA_2019_8_1_a5
ER  - 
%0 Journal Article
%A A. N. Kirillov
%T The method of normal local stabilization
%J Problemy analiza
%D 2019
%P 72-83
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/PA_2019_8_1_a5/
%G en
%F PA_2019_8_1_a5
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/

[1] Davis C., “Theory of positive linear dependence”, Amer. J. Math., 76 (1954), 733–746 | DOI | MR | Zbl

[2] Utkin V. I., Sliding Modes in Control and Optimization, Springer-Verlag, 1992 | MR | Zbl

[3] Bartolini G., Pisano A., Punta E., Usai E., “A survey of applications of second order sliding mode control to mechanical systems”, Int. J. Control, 76 (2003), 875–892 | DOI | MR | Zbl

[4] Bhat S. P., Bernstein D. S., “Finite-time stability of autonomous systems”, SIAM J. Control Optim., 38, 751–766 | DOI | MR | Zbl

[5] Kirillov A. N., “The stabilization problem for certain class of ecological systems”, Int. J. Softw. Eng. Knowl. Eng., 1997, no. 7, 247–251 | DOI

[6] Petrov N. N., “Local controllability of autonomous systems”, Differ. Uravn., 1968, no. 7, 1218–1232 (in Russian) | MR | Zbl

[7] Petrov N. N., “A solution of a certain problem in control theory”, Differ. Uravn., 1969, no. 5, 962–963 (in Russian) | MR | Zbl