Let and be two smooth vector fields on , globally asymptotically stable at the origin. We give some sufficient and some necessary conditions on the topology of the set where and are parallel for global asymptotic stability of the nonautonomous and nonlinear control system
where is an arbitrary measurable function. Such conditions can be verified without any integration or construction of a Lyapunov function, and are robust.
Soient et deux champs de vecteurs lisses sur globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où et sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonome
où le contrôle est une fonction mesurable arbitraire de dans . Les conditions données ne nécessitent aucune intégration ou construction d’une fonction de Lyapunov pour être vérifiées, et sont robustes.
@article{TSG_2009-2010__28__1_0, author = {Ugo Boscain and Gr\'egoire Charlot and Mario Sigalotti}, title = {Stabilit\'e des syst\`emes \`a commutations du plan}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {1--12}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {28}, year = {2009-2010}, doi = {10.5802/tsg.275}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.275/} }
TY - JOUR AU - Ugo Boscain AU - Grégoire Charlot AU - Mario Sigalotti TI - Stabilité des systèmes à commutations du plan JO - Séminaire de théorie spectrale et géométrie PY - 2009-2010 SP - 1 EP - 12 VL - 28 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.275/ DO - 10.5802/tsg.275 LA - fr ID - TSG_2009-2010__28__1_0 ER -
%0 Journal Article %A Ugo Boscain %A Grégoire Charlot %A Mario Sigalotti %T Stabilité des systèmes à commutations du plan %J Séminaire de théorie spectrale et géométrie %D 2009-2010 %P 1-12 %V 28 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.275/ %R 10.5802/tsg.275 %G fr %F TSG_2009-2010__28__1_0
Ugo Boscain; Grégoire Charlot; Mario Sigalotti. Stabilité des systèmes à commutations du plan. Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 1-12. doi : 10.5802/tsg.275. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.275/
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