Contrôlabilité des systèmes bilinéaires dans le plan
Publications du Département de mathématiques (Lyon), no. 3A (1985), pp. 1-56.
@article{PDML_1985___3A_1_0,
     author = {Adda, Philippe},
     title = {Contr\^olabilit\'e des syst\`emes bilin\'eaires dans le plan},
     journal = {Publications du D\'epartement de math\'ematiques (Lyon)},
     pages = {1--56},
     publisher = {Universit\'e Claude Bernard - Lyon 1},
     number = {3A},
     year = {1985},
     zbl = {0664.93004},
     language = {fr},
     url = {http://www.numdam.org/item/PDML_1985___3A_1_0/}
}
TY  - JOUR
AU  - Adda, Philippe
TI  - Contrôlabilité des systèmes bilinéaires dans le plan
JO  - Publications du Département de mathématiques (Lyon)
PY  - 1985
DA  - 1985///
SP  - 1
EP  - 56
IS  - 3A
PB  - Université Claude Bernard - Lyon 1
UR  - http://www.numdam.org/item/PDML_1985___3A_1_0/
UR  - https://zbmath.org/?q=an%3A0664.93004
LA  - fr
ID  - PDML_1985___3A_1_0
ER  - 
Adda, Philippe. Contrôlabilité des systèmes bilinéaires dans le plan. Publications du Département de mathématiques (Lyon), no. 3A (1985), pp. 1-56. http://www.numdam.org/item/PDML_1985___3A_1_0/

[1] V. Arnold, Méthodes mathématiques de la mécanique classique Ed. Mir. Moscou. | Zbl 0385.70001

[2] J. Bailleul, Geometric methods for non linear optimal control problems. J. of Optim. theory and applications vol. 25 n° 4 (1978), p. 519-548. | MR 511616

[3] The geometry of homogeneous polynomial dynamical systems. - Non linear analysis, theory, methods and applications vol. 4 (1980), p. 879-900. | MR 586853 | Zbl 0473.34022

[4] B. Bonnard, Controlabilité et observabilité d'une certaine classe de systèmes linéaires (à paraitre) - Note LAG, Grenoble 82-09.

[5] Controle de l'attitude d'un satellite rigide. RAIRO série automatique vol. 16 n° 1 (1982) p. 85-93. | Zbl 0483.93022

[6] Controllability of mechanical control systems on Lie groups (to appear).

[7] W. Boothby, A transitivity problem from control theory - J. Diff ; Eq. 17 (1975) p. 296-307. | MR 436210 | Zbl 0316.93006

[8] W. Boothby and E. N. Wilson, Determination of the transitivity of bilinear systems - SIAM J. Control 17 (1979) p. 212- | MR 525022 | Zbl 0406.93037

[9] C. Bruni, D. Dipillo and G. Koch, Bilinear systems : on appealing class of nearly linear systems in theory and applications. IEEE Trans. Automat. Control. Vol. 19 (1974) p. 334-348. | MR 414174 | Zbl 0285.93015

[10] M. Denis-Papin, A. Kaufmann, Cours de calcul opérationnel appliqué. Albin Michel (1967). | MR 352892 | Zbl 0038.26802

[11] M. Fliess, Séries de Volterra et séries formelles non commutatives. C.R. Acad. Sc. Paris (1975) p. 965-967. | MR 381784 | Zbl 0309.93028

[12] J. P. Gauthier, G. Bonnard, A theorem of controllability for bilinear system - Note interne LAG Grenoble 81-04.

[13] H. Hermes, On the synthesis of a stabilizing feedback control via Lie algebraïc methods. SIAM J. Control, vol. 18 n° 4 (1980), p. 352-360. | MR 579546 | Zbl 0477.93046

[14] R. Hirschorn, Controllability in non linear systems. J. Diff ; Eq. 19 (1975) p. 46-61. | Zbl 0315.93002

[15] L. R. Hunt, Controllability of general nonlinear systems. Math. systems theory 12 (1979) p. 361-370. | MR 541864 | Zbl 0394.93010

[16] V. Jurdjevic and I. Kupka Control systems on semi-simple Lie groups and their homogeneous spaces, Ann. Institut Fourier Tome 3, fasc. 4 (1981) p. 151-179. | Numdam | MR 644347 | Zbl 0453.93011

[17] Control systems subordinated to a group action : Accessibility. J. Diff. Eq. vol. 39 n° 2 (1981) p. 186-211. | MR 607781 | Zbl 0531.93008

[18] V. Jurdjevic and G. Sallet, Controllability property of affine systems (to appear) SIAM J. on Control. | Zbl 0549.93010

[19] A. J. Krener, A generalization of Chow's theorem and the bang-bang theorem to non linear control problems. SIAM J. Control 12 (1974) p. 43-52. | MR 383206 | Zbl 0243.93008

[20] I. Kupka, Thèse. Université de Dijon (1978).

[21] C. Lobry Bases mathématiques de la théorie des systèmes asservis non linéaires. (non publié).

[22] R. I. Rink and R. R. Mohler, Completely controllable bilinear systems. SIAM J. Control vol. 6 n° 3 (1968). | MR 255270 | Zbl 0159.13001

[23] G. Sallet, Extension techniques. Encyclopaedia of control. Pergamon press. Madan Singh.

[24] Encadrement des ensembles d'accessibilité en temps exact. Application à la théorie des systèmes (à paraître).

[25] G. Sallet, Sur la structure de l'ensemble d'accessibilité de certains systèmes. Application à l'équivalence des systèmes, (à paraître). | Zbl 0574.49023

[26] B. V. Schmitt, Sur la structure de l'équation de Duffing sans dissipation. SIAM J. Appl. Math. vol. 42 (1982) p. 868-894. | MR 665391 | Zbl 0515.34031

[27] M. B. Surymarayana, Linear control problems with total differential equations without convexity. American Math. Soc. (1974). | Zbl 0297.49005

[28] H. J. Sussmann, Semi-groups representations, bilinear approximation of input-output maps and generalized inputs. Mathematical systems theory and Lecture notes in Economics and Math. systems n° 131 p. 172-191. G. Marchesin and S.K. Mitter Ed. | MR 683616 | Zbl 0353.93025

[29] Some properties of vector fields systems that are not altered by small perturbations. J. Diff. Eq. Vol. 20 n° 2 (1976) p. 292-315. | MR 394756 | Zbl 0346.49036

[30] A sufficient condition for local controllability. SIAM J. control and Opt. vol. 16 n° 5 (3978) p. 790-802. | MR 527718 | Zbl 0391.93004

[31] H. J. Sussmann and V. Jurdjevic, Controllability of non linear systems. J. DIFF. Eq. 12 (1972) p. 95-116. | MR 338882 | Zbl 0242.49040

[32] W.M. Wonham, Linear multivariable control. A geometric approach. Lecture notes in Economics and Maths systems n° 101. M. Beckmann and H.P. Kiinzi Ed. | MR 770574 | Zbl 0314.93007