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Stabilisation des systèmes contrôlables et observables
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 4 (1995) no. 1, pp. 31-59.
@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},
     doi = {10.5802/afst.791},
     zbl = {0839.93061},
     mrnumber = {1344716},
     language = {fr},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.791/}
}
Jean-Michel Coron. Stabilisation des systèmes contrôlables et observables. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 4 (1995) no. 1, pp. 31-59. doi : 10.5802/afst.791. https://afst.centre-mersenne.org/articles/10.5802/afst.791/

[1] Agrechev (A.A.) et Gramkrelidze (R.V.) .- Local controllability and semigroup of diffeomorphisms, Preprint, Steklov Math. Institute, 1993. | MR 1232941

[2] Bianchini (R.M.) et Stefani (G.) .- Sufficient conditions of local controllability, Proc. of 25th conference on Décision and Control, Athens, Greece (Dec. 1986), pp. 967-970.

[3] Bianchini (R.M.) et Stefani (G.) .- Controllability along a trajectory: a variational approach, SIAM J. Control and Optimization 31 (1993), pp. 900-927. | MR 1227538 | Zbl 0797.49015

[4] Brockett (R.W.) . - 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 708502 | Zbl 0528.93051

[5] Brunovsky (P.) . - Local controllability of odd systems, Banach Center Publications 1 (1974), pp. 39-45. | Zbl 0344.93016

[6] Chow (W.L.) .- Uber systeme von linearen partiellen differentialgleichungen ester ordnung, Math. Ann. 117 (1940-41), pp. 98-105. | JFM 65.0398.01 | MR 1880 | Zbl 0022.02304

[7] Coron (J.-M.) .- A necessary condition for feedback stabilization, Systems and Control Letters 14 (1990), pp. 227-232. | MR 1049357 | Zbl 0699.93075

[8] Coron (J.-M.) .- Global asymptotic stabilization for controllable systems without drift, Math. Control Signals and Systems 5 (1992), pp. 295-312. | MR 1164379 | Zbl 0760.93067

[9] Coron (J.-M.) .- 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] Coron (J.-M.) . - Linearized control systems and applications to smooth stabilization, SIAM J. Control and Optimization 32 (1994), pp. 358-386. | MR 1261144 | Zbl 0796.93097

[11] Coron (J.-M.) .- 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 1327239 | Zbl 0828.93054

[12] Coron (J.-M.) .- Stabilization of controllable systems, Prépublication, ENS de Cachan (avril 1993). | MR 1359027

[13] Coron (J.-M.) .- Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C.R. Acad. Sci. Paris 317 (1993), pp. 271-276. | MR 1233425 | Zbl 0781.76013

[14] Coron (J.-M.) .- On the stabilization by output feedback law of controllable and observable systems, Prépublication, ENS de Cachan (octobre 1993). | MR 1359027

[15] Coron (J.-M.) et Pomet (J.-B.) .- 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.

[16] Coron (J.-M.) et Praly (L.) .- Adding an integrator for the stabilization problem, Systems and Control Letters 17 (1991), pp. 89-104. | MR 1120754 | Zbl 0747.93072

[17] Coron (J.-M.) et Rosier (L.) .- A relation between continuous time-varying and discontinuous feedback stabilization, SIAM Journal Math. Syst. Estimation and Control 4 (1994), pp. 67-84. | MR 1298548 | Zbl 0925.93827

[18] Dayawansa (W.P.), Martin (C.) et Knowles (G.) .- Asymptotic stabilization of a class of smooth two dimensional systems, SIAM J. on Control and Optimization 28 (1990), pp. 1321-1349. | MR 1075206 | Zbl 0731.93076

[19] Esfandiari (F.) et Khalil (H.K.) .- Output feedback stabilization of fully linearizable systems, International Journal of Control (1992), à paraître. | MR 1187838 | Zbl 0762.93069

[20] Hermann (R.) et Krener (A.J.) .- Nonlinear controllability and observability, IEEE Transactions on Automatic Control 22 (1977), pp. 728-740. | MR 476017 | Zbl 0396.93015

[21] Hermes (H.) .- 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 222424

[22] Hermes (H.) .- On the synthesis of a stabilizing feedback control via Lie algebraic methods, SIAM J. on Control and Optimization 18 (1980), pp. 352-361. | MR 579546 | Zbl 0477.93046

[23] Isidori (A.) .- Nonlinear Control Systems (Second edition), Springer-Verlag, Berlin - Heidelberg (1989). | MR 1015932

[24] Kawski (M.) .- Stabilization of nonlinear systems in the plane, Systems and Control Letters 12 (1989), pp. 169-175. | MR 985567 | Zbl 0666.93103

[25] Kawski (M.) . - 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 1061394 | Zbl 0703.93013

[26] Kurzweil (J.) .- On the inversion of Ljapunov's second theorem on stability of motion, Amer. Math. Soc. 24 (1956), pp. 19-77. | Zbl 0127.30703

[27] Landau (L.) et Lifchitz (E.) .- Physique théorique, mécanique Mir, Moscou (1988). | MR 1085484

[28] Lozano-Leal (R.) .- Robust adaptative regulation without persistent excitation, IEEE Transactions on Automatic Control 34 (1989), pp. 1260-1267. | MR 1029376 | Zbl 0689.93038

[29] Mazenc (F.) et Praly (L.) .- Global stabilization for nonlinear systems, Preprint, ENSMP, CAS (janvier 1993).

[30] Mazenc (F.), Praly (L.) et Dayawansa (W.P.) .- Global stabilization by output feedback: examples and counter-examples, Preprint, ENSMP, CAS (avril 1993) à paraître dans Systems and Control Letters. | MR 1287604 | Zbl 0816.93068

[31] Pomet (J.-B.) . - 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 1149359 | Zbl 0744.93084

[32] Rosier (L.) .- Inverse of Lyapunov's second theorem for measurable functions, NOLCOS'92, M. Fliess (éd.), Bordeaux (24-26 juin 1992), pp. 655-660.

[33] Sontag (E.D.) .- Conditions for abstract nonlinear regulation, Information and Control 51 (1981), pp. 105-127. | MR 686833 | Zbl 0544.93058

[34] Sontag (E.D.) . - Finite dimensional open-loop control generators for nonlinear systems, International Journal of Control 47 (1988), pp. 537-556. | MR 929174 | Zbl 0641.93035

[35] Sontag (E.D.) .- Mathematical control Theory, Text in Applied Mathematics 6, Springer-Verlag, New-York - Berlin - Heidelberg (1990). | MR 1070569 | Zbl 0703.93001

[36] Sontag (E.D.) . - Universal nonsingular controls, Systems and Control Letters 19 (1992), pp. 221-224. | MR 1180510 | Zbl 0763.93038

[37] Sontag (E.D.) et Sussmann (H.J.) .- Remarks on continuous feedback, IEEE CDC, Albuquerque 2 (1980), pp. 916-921.

[38] Sussmann (H.J.) .- Single-input observability of continuous-time systems, Math. Systems Theory 12 (1979), pp. 371-393. | MR 541865 | Zbl 0422.93019

[39] Sussmann (H.J.) .- Lie brackets and local controllability: a sufficient condition for scalar input systems, SIAM J. on Control and Optimization 21 (1983), pp. 686-713. | MR 710995 | Zbl 0523.49026

[40] Sussmann (H.J.) .- A general theorem on local controllability, SIAM J. on Control and Optimization 25 (1987), pp. 158-194. | MR 872457 | Zbl 0629.93012

[41] Sussmann (H.J.) . - Subanalytic sets and feedback control, J. Differential Equations 31 (1979), pp. 31-52. | MR 524816 | Zbl 0407.93010

[42] Sussmann (H.J.) et Jurdjevic (V.) .- Controllability of nonlinear systems, Journal Differential Equations 12 (1972), pp. 95-116. | MR 338882 | Zbl 0242.49040

[43] Teel (A.) et Praly (L.) .- Global stabilizability and observability imply semiglobal stabilizability by output feedback, Prépublication, Fontainebleau (janvier 1993) à paraître dans SIAM J. on Control and Optimization. | MR 1274906

[44] Wang (S.H.) .- Stabilization of decentralized control systems via time-varying controllers, IEEE Transactions on Automatic Control, AC 27 (1982), pp. 741-744. | Zbl 0478.93043

[45] Wang (Y.) et Sontag (E.D.) .- Order of input/output differential equations and state space dimensions, Prépublication, Florida Atlantic University, (mars 1993).

[46] Whitehead (G.W.) .- Elements of Homotopy Theory, Graduate Texts in Mathematics 61, Springer-Verlag, New-York - Berlin - Heidelberg (1978). | MR 516508 | Zbl 0406.55001

[47] Whitney (H.) et Bruhat (F.) .- Quelques propriétés fondamentales des ensembles analytiques réels, Comm. Math. Helv. 33 (1959), pp. 132-160. | MR 102094 | Zbl 0100.08101