@article{AFST_1995_6_4_1_31_0, author = {Coron, Jean-Michel}, title = {Stabilisation des syst\`emes contr\^olables et observables}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {31--59}, publisher = {Universit\'e Paul Sabatier}, address = {Toulouse}, volume = {6e s{\'e}rie, 4}, number = {1}, year = {1995}, mrnumber = {1344716}, zbl = {0839.93061}, language = {fr}, url = {http://www.numdam.org/item/AFST_1995_6_4_1_31_0/} }
TY - JOUR AU - Coron, Jean-Michel TI - Stabilisation des systèmes contrôlables et observables JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1995 SP - 31 EP - 59 VL - 4 IS - 1 PB - Université Paul Sabatier PP - Toulouse UR - http://www.numdam.org/item/AFST_1995_6_4_1_31_0/ LA - fr ID - AFST_1995_6_4_1_31_0 ER -
%0 Journal Article %A Coron, Jean-Michel %T Stabilisation des systèmes contrôlables et observables %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1995 %P 31-59 %V 4 %N 1 %I Université Paul Sabatier %C Toulouse %U http://www.numdam.org/item/AFST_1995_6_4_1_31_0/ %G fr %F AFST_1995_6_4_1_31_0
Coron, Jean-Michel. Stabilisation des systèmes contrôlables et observables. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 4 (1995) no. 1, pp. 31-59. http://www.numdam.org/item/AFST_1995_6_4_1_31_0/
[1] Local controllability and semigroup of diffeomorphisms, Preprint, Steklov Math. Institute, 1993. | MR
) et ) .-[2] Sufficient conditions of local controllability, Proc. of 25th conference on Décision and Control, Athens, Greece (Dec. 1986), pp. 967-970.
) et ) .-[3] Controllability along a trajectory: a variational approach, SIAM J. Control and Optimization 31 (1993), pp. 900-927. | MR | Zbl
) et ) .-[4] Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, R. W. Brocket, R. S. Millman et H. J. Sussmann (eds), Birkhäuser, Basel-Boston, 1983. | MR | Zbl
) . -[5] Local controllability of odd systems, Banach Center Publications 1 (1974), pp. 39-45. | Zbl
) . -[6] Uber systeme von linearen partiellen differentialgleichungen ester ordnung, Math. Ann. 117 (1940-41), pp. 98-105. | JFM | MR | Zbl
) .-[7] A necessary condition for feedback stabilization, Systems and Control Letters 14 (1990), pp. 227-232. | MR | Zbl
) .-[8] Global asymptotic stabilization for controllable systems without drift, Math. Control Signals and Systems 5 (1992), pp. 295-312. | MR | Zbl
) .-[9] Links between local controllability and local continuous stabilization, Preprint, Université Paris-Sud et ETH Zürich (oct. 1991), et NOLCOS'92, M. Fliess (éd.), Bordeaux (24-26 juin 1992), pp. 477-482.
) .-[10] Linearized control systems and applications to smooth stabilization, SIAM J. Control and Optimization 32 (1994), pp. 358-386. | MR | Zbl
) . -[11] On the stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws, Prépublication, ENS de Cachan (octobre 1992) à paraître dans SIAM J. Control and Optimization. | MR | Zbl
) .-[12] Stabilization of controllable systems, Prépublication, ENS de Cachan (avril 1993). | MR
) .-[13] Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C.R. Acad. Sci. Paris 317 (1993), pp. 271-276. | MR | Zbl
) .-[14] On the stabilization by output feedback law of controllable and observable systems, Prépublication, ENS de Cachan (octobre 1993). | MR
) .-[15] A remark on the design of time-varying stabilizing feedback laws for controllable systems without drift, NOLCOS'92, M. Fliess (éd.), Bordeaux (24-26 juin 1992), pp. 413-417.
) et ) .-[16] Adding an integrator for the stabilization problem, Systems and Control Letters 17 (1991), pp. 89-104. | MR | Zbl
) et ) .-[17] A relation between continuous time-varying and discontinuous feedback stabilization, SIAM Journal Math. Syst. Estimation and Control 4 (1994), pp. 67-84. | MR | Zbl
) et ) .-[18] Asymptotic stabilization of a class of smooth two dimensional systems, SIAM J. on Control and Optimization 28 (1990), pp. 1321-1349. | MR | Zbl
), ) et ) .-[19] Output feedback stabilization of fully linearizable systems, International Journal of Control (1992), à paraître. | MR | Zbl
) et ) .-[20] Nonlinear controllability and observability, IEEE Transactions on Automatic Control 22 (1977), pp. 728-740. | MR | Zbl
) et ) .-[21] Discontinuous vector fields and feedback control, Differential Equations and Dynamical Systems, J. K. Hale et J.-P. La Salle (éds.), Academic Press, New-York - London (1967). | MR
) .-[22] On the synthesis of a stabilizing feedback control via Lie algebraic methods, SIAM J. on Control and Optimization 18 (1980), pp. 352-361. | MR | Zbl
) .-[23] Nonlinear Control Systems (Second edition), Springer-Verlag, Berlin - Heidelberg (1989). | MR
) .-[24] Stabilization of nonlinear systems in the plane, Systems and Control Letters 12 (1989), pp. 169-175. | MR | Zbl
) .-[25] Higher-order small-time local controllability, Nonlinear Controllability and Optimal Control, H. J. Sussmann (éd.), Monographs and Textbooks in Pure and Applied Mathematics, 113, Marcel-Dekker, Inc., New-York (1990), pp. 431-467. | MR | Zbl
) . -[26] On the inversion of Ljapunov's second theorem on stability of motion, Amer. Math. Soc. 24 (1956), pp. 19-77. | Zbl
) .-[27] Physique théorique, mécanique Mir, Moscou (1988). | MR
) et ) .-[28] Robust adaptative regulation without persistent excitation, IEEE Transactions on Automatic Control 34 (1989), pp. 1260-1267. | MR | Zbl
) .-[29] Global stabilization for nonlinear systems, Preprint, ENSMP, CAS (janvier 1993).
) et ) .-[30] Global stabilization by output feedback: examples and counter-examples, Preprint, ENSMP, CAS (avril 1993) à paraître dans Systems and Control Letters. | MR | Zbl
), ) et ) .-[31] Explicit design of time-varying stabilizing control law for a class of controllable systems without drift, Systems and Control Letters 18 (1992), pp. 147-158. | MR | Zbl
) . -[32] Inverse of Lyapunov's second theorem for measurable functions, NOLCOS'92, M. Fliess (éd.), Bordeaux (24-26 juin 1992), pp. 655-660.
) .-[33] Conditions for abstract nonlinear regulation, Information and Control 51 (1981), pp. 105-127. | MR | Zbl
) .-[34] Finite dimensional open-loop control generators for nonlinear systems, International Journal of Control 47 (1988), pp. 537-556. | MR | Zbl
) . -[35] Mathematical control Theory, Text in Applied Mathematics 6, Springer-Verlag, New-York - Berlin - Heidelberg (1990). | MR | Zbl
) .-[36] Universal nonsingular controls, Systems and Control Letters 19 (1992), pp. 221-224. | MR | Zbl
) . -[37] Remarks on continuous feedback, IEEE CDC, Albuquerque 2 (1980), pp. 916-921.
) et ) .-[38] Single-input observability of continuous-time systems, Math. Systems Theory 12 (1979), pp. 371-393. | MR | Zbl
) .-[39] Lie brackets and local controllability: a sufficient condition for scalar input systems, SIAM J. on Control and Optimization 21 (1983), pp. 686-713. | MR | Zbl
) .-[40] A general theorem on local controllability, SIAM J. on Control and Optimization 25 (1987), pp. 158-194. | MR | Zbl
) .-[41] Subanalytic sets and feedback control, J. Differential Equations 31 (1979), pp. 31-52. | MR | Zbl
) . -[42] Controllability of nonlinear systems, Journal Differential Equations 12 (1972), pp. 95-116. | MR | Zbl
) et ) .-[43] Global stabilizability and observability imply semiglobal stabilizability by output feedback, Prépublication, Fontainebleau (janvier 1993) à paraître dans SIAM J. on Control and Optimization. | MR
) et ) .-[44] Stabilization of decentralized control systems via time-varying controllers, IEEE Transactions on Automatic Control, AC 27 (1982), pp. 741-744. | Zbl
) .-[45] Order of input/output differential equations and state space dimensions, Prépublication, Florida Atlantic University, (mars 1993).
) et ) .-[46] Elements of Homotopy Theory, Graduate Texts in Mathematics 61, Springer-Verlag, New-York - Berlin - Heidelberg (1978). | MR | Zbl
) .-[47] Quelques propriétés fondamentales des ensembles analytiques réels, Comm. Math. Helv. 33 (1959), pp. 132-160. | MR | Zbl
) et ) .-