Stabilisation des systèmes contrôlables et observables

Jean-Michel Coron

Annales de la Faculté des sciences de Toulouse : Mathématiques (1995)

  • Volume: 4, Issue: 1, page 31-59
  • ISSN: 0240-2963

How to cite

top

Coron, Jean-Michel. "Stabilisation des systèmes contrôlables et observables." Annales de la Faculté des sciences de Toulouse : Mathématiques 4.1 (1995): 31-59. <http://eudml.org/doc/73343>.

@article{Coron1995,
author = {Coron, Jean-Michel},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {stabilization; periodic; continuous; dynamic output feedback},
language = {fre},
number = {1},
pages = {31-59},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Stabilisation des systèmes contrôlables et observables},
url = {http://eudml.org/doc/73343},
volume = {4},
year = {1995},
}

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
PB - UNIVERSITE PAUL SABATIER
VL - 4
IS - 1
SP - 31
EP - 59
LA - fre
KW - stabilization; periodic; continuous; dynamic output feedback
UR - http://eudml.org/doc/73343
ER -

References

top
  1. [1] Agrechev ( A.A.) et Gramkrelidze ( R.V.) .— Local controllability and semigroup of diffeomorphisms, Preprint, Steklov Math. Institute, 1993. MR1232941
  2. [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. [3] Bianchini ( R.M.) et Stefani ( G.) .— Controllability along a trajectory: a variational approach, SIAM J. Control and Optimization31 (1993), pp. 900-927. Zbl0797.49015MR1227538
  4. [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. Zbl0528.93051MR708502
  5. [5] Brunovsky ( P.) . - Local controllability of odd systems, Banach Center Publications1 (1974), pp. 39-45. Zbl0344.93016
  6. [6] Chow ( W.L.) .— Uber systeme von linearen partiellen differentialgleichungen ester ordnung, Math. Ann.117 (1940-41), pp. 98-105. Zbl0022.02304MR1880JFM65.0398.01
  7. [7] Coron ( J.-M.) .— A necessary condition for feedback stabilization, Systems and Control Letters14 (1990), pp. 227-232. Zbl0699.93075MR1049357
  8. [8] Coron ( J.-M.) .— Global asymptotic stabilization for controllable systems without drift, Math. Control Signals and Systems5 (1992), pp. 295-312. Zbl0760.93067MR1164379
  9. [9] Coron ( J.-M.) .— Links between local controllability and local continuous stabilization, Preprint, Université Paris-Sud et ETHZürich (oct. 1991), et NOLCOS'92, M. Fliess (éd.), Bordeaux (24-26 juin 1992), pp. 477-482. 
  10. [10] Coron ( J.-M.) . — Linearized control systems and applications to smooth stabilization, SIAM J. Control and Optimization32 (1994), pp. 358-386. Zbl0796.93097MR1261144
  11. [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. Zbl0828.93054MR1327239
  12. [12] Coron ( J.-M.) .— Stabilization of controllable systems, Prépublication, ENS de Cachan (avril 1993). MR1359027
  13. [13] Coron ( J.-M.) .— Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C.R. Acad. Sci.Paris317 (1993), pp. 271-276. Zbl0781.76013MR1233425
  14. [14] Coron ( J.-M.) .— On the stabilization by output feedback law of controllable and observable systems, Prépublication, ENS de Cachan (octobre 1993). MR1359027
  15. [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. [16] Coron ( J.-M.) et Praly ( L.) .— Adding an integrator for the stabilization problem, Systems and Control Letters17 (1991), pp. 89-104. Zbl0747.93072MR1120754
  17. [17] Coron ( J.-M.) et Rosier ( L.) .— A relation between continuous time-varying and discontinuous feedback stabilization, SIAM Journal Math. Syst. Estimation and Control4 (1994), pp. 67-84. Zbl0925.93827MR1298548
  18. [18] Dayawansa ( W.P.), Martin ( C.) et Knowles ( G.) .— Asymptotic stabilization of a class of smooth two dimensional systems, SIAM J. on Control and Optimization28 (1990), pp. 1321-1349. Zbl0731.93076MR1075206
  19. [19] Esfandiari ( F.) et Khalil ( H.K.) .— Output feedback stabilization of fully linearizable systems, International Journal of Control (1992), à paraître. Zbl0762.93069MR1187838
  20. [20] Hermann ( R.) et Krener ( A.J.) .— Nonlinear controllability and observability, IEEE Transactions on Automatic Control22 (1977), pp. 728-740. Zbl0396.93015MR476017
  21. [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). MR222424
  22. [22] Hermes ( H.) .— On the synthesis of a stabilizing feedback control via Lie algebraic methods, SIAM J. on Control and Optimization18 (1980), pp. 352-361. Zbl0477.93046MR579546
  23. [23] Isidori ( A.) .— Nonlinear Control Systems (Second edition), Springer-Verlag, Berlin - Heidelberg (1989). MR1015932
  24. [24] Kawski ( M.) .— Stabilization of nonlinear systems in the plane, Systems and Control Letters12 (1989), pp. 169-175. Zbl0666.93103MR985567
  25. [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. Zbl0703.93013MR1061394
  26. [26] Kurzweil ( J.) .— On the inversion of Ljapunov's second theorem on stability of motion, Amer. Math. Soc.24 (1956), pp. 19-77. Zbl0127.30703
  27. [27] Landau ( L.) et Lifchitz ( E.) .— Physique théorique, mécaniqueMir, Moscou (1988). MR1085484
  28. [28] Lozano-Leal ( R.) .— Robust adaptative regulation without persistent excitation, IEEE Transactions on Automatic Control34 (1989), pp. 1260-1267. Zbl0689.93038MR1029376
  29. [29] Mazenc ( F.) et Praly ( L.) .— Global stabilization for nonlinear systems, Preprint, ENSMP, CAS (janvier 1993). 
  30. [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. Zbl0816.93068MR1287604
  31. [31] Pomet ( J.-B.) . — Explicit design of time-varying stabilizing control law for a class of controllable systems without drift, Systems and Control Letters18 (1992), pp. 147-158. Zbl0744.93084MR1149359
  32. [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. [33] Sontag ( E.D.) .— Conditions for abstract nonlinear regulation, Information and Control51 (1981), pp. 105-127. Zbl0544.93058MR686833
  34. [34] Sontag ( E.D.) . — Finite dimensional open-loop control generators for nonlinear systems, International Journal of Control47 (1988), pp. 537-556. Zbl0641.93035MR929174
  35. [35] Sontag ( E.D.) .— Mathematical control Theory, Text in Applied Mathematics6, Springer-Verlag, New-York - Berlin - Heidelberg (1990). Zbl0703.93001MR1070569
  36. [36] Sontag ( E.D.) . — Universal nonsingular controls, Systems and Control Letters19 (1992), pp. 221-224. Zbl0763.93038MR1180510
  37. [37] Sontag ( E.D.) et Sussmann ( H.J.) .— Remarks on continuous feedback, IEEE CDC, Albuquerque2 (1980), pp. 916-921. 
  38. [38] Sussmann ( H.J.) .— Single-input observability of continuous-time systems, Math. Systems Theory12 (1979), pp. 371-393. Zbl0422.93019MR541865
  39. [39] Sussmann ( H.J.) .— Lie brackets and local controllability: a sufficient condition for scalar input systems, SIAM J. on Control and Optimization21 (1983), pp. 686-713. Zbl0523.49026MR710995
  40. [40] Sussmann ( H.J.) .— A general theorem on local controllability, SIAM J. on Control and Optimization25 (1987), pp. 158-194. Zbl0629.93012MR872457
  41. [41] Sussmann ( H.J.) . — Subanalytic sets and feedback control, J. Differential Equations31 (1979), pp. 31-52. Zbl0407.93010MR524816
  42. [42] Sussmann ( H.J.) et Jurdjevic ( V.) .— Controllability of nonlinear systems, Journal Differential Equations12 (1972), pp. 95-116. Zbl0242.49040MR338882
  43. [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. MR1274906
  44. [44] Wang ( S.H.) .— Stabilization of decentralized control systems via time-varying controllers, IEEE Transactions on Automatic Control, AC 27 (1982), pp. 741-744. Zbl0478.93043
  45. [45] Wang ( Y.) et Sontag ( E.D.) .— Order of input/output differential equations and state space dimensions, Prépublication, Florida Atlantic University, (mars 1993). 
  46. [46] Whitehead ( G.W.) .— Elements of Homotopy Theory, Graduate Texts in Mathematics61, Springer-Verlag, New-York - Berlin - Heidelberg (1978). Zbl0406.55001MR516508
  47. [47] Whitney ( H.) et Bruhat ( F.) .— Quelques propriétés fondamentales des ensembles analytiques réels, Comm. Math. Helv.33 (1959), pp. 132-160. Zbl0100.08101MR102094

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.