Filtrations in feedback synthesis: Part I - Systems and feedbacks

Forum Mathematicum

Volumn 10, Issue 2, 1998, Pages 147-174

  Delaleau, Emmanuel ^a   Pereira Da Silva, Paulo Sérgio ^b  

^a UNIV PARIS SUD   (France)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032222152     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.10.2.147     Document Type: Article

References (70)

1. Aït Amirat, Y., Diop, S. and Moog, C.H.: Un nouvel algorithme de structure. C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 103-108
2. Andiarti, R.: Invariances généralisées pour les systèmes non linéaires et applications. Thèse de Doctorat, Université de Nantes/École Centrale de Nantes, 1995
3. Atiyah, M.F. and Macdonald, I.G.: Introduction to Commutative Algebra. Addison Wesley, Reading, MA 1969
4. Basile, G. and Marro, G.: Controlled and Conditionned Invariants in Linear System Theory. Prentice-Hall, New Jersey 1992
5. Bourbaki, N.: Éléments de mathématique: algèbre commutative. Chapitres 3 et 4. Hermann, Paris 1961
6. Bourbaki, N.: Éléments de mathématique: algèbre, Chapitres 4 à 7. Masson, Paris 1981
7. Brunovský, P.: A classification of linear controllable systems. Kybernetika (Prague) 6 (1980), 173-187
8. Cartan, É.: Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes. Bull. Soc. Math. France 42 (1914), 12-48
9. Cohn. P. M.: Free rings and their relations. Academic Press, London, 2nd edition, 1985
10. Conte, G., Perdon, A. M. and Moog, C. H.: Towards a notion of canonical form for nonlinear systems. In B. Jakubczyk, W. Respondek, and T. Rzeżuchowski, editors. Geometry in Nonlinear Control and Differential Inclusions, volume 32 of Banach Center Publ., pages 149-165, Warszawa 1995
11. Cox, D., Little, J. and O'Shea, D.: Ideals, Varieties and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer-Verlag, New York 1992
12. Delaleau, E.: Sur les dérivées de l'entrée en représentation et commande des systèmes non linéaires. Thèse de Doctorat, Université Paris XI, 1993
13. Delaleau, E. and Fliess, M.: Algorithme de structure, filtrations et découplage. C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 101-106
14. Delaleau, E. and Fliess, M.: An algebraic interpretation of the structure algorithm with an application to feedback decoupling. In M. Fliess, editor, Nonlinear Control Systems Design 1992, Selected Papers from the 2nd IFAC Symposium, pages 489-494, Oxford 1993, Pergamon Press
15. Delaleau, E. and Fliess, M.: Nonlinear disturbance rejection by quasi-static state feedback. In U. Helmke, R. Mennicken, and J. Saurer, editors, Systems and Networks: Mathematical Theory and Applications (MTNS '93, Volume II, Invited and Contributed Papers), pages 109-112, Berlin 1994, Akademie Verlag
16. Delaleau, E. and Pereira da Silva, P.S.: Conditions de rang pour le rejet dynamique de perturbations. C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 1121-1126
17. Delaleau, E. and Pereira da Silva, P.S.: Rank conditions for the dynamic disturbance decoupling problem. In Proc. 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, pages 1784-1789, 1994
18. Delaleau, E. and Pereira da Silva, P.S.: Filtrations in feedback synthesis: Part II-input-output decoupling and disturbance decoupling. Forum Math. 10 (1998), 259-275
19. Delaleau, E. and Respondek, W.: Lowering the orders of derivatives of controls in generalized state space systems. J. Math. Systems Estim. Control 5 (1995), 375-378
20. Delaleau, E. and Rudolph, J.: Decoupling and linearization by quasi-static feedback of generalized states. In A. Isidori, S. Bittanti, E. Mosca, A. De Luca, and M.D.Di Benedetto, editors, Proc. 3rd European Control Conference, pages 1069-1074, Rome 1995
21. Delaleau, E. and Rudolph, J.: An intrinsic characterization of properness for linear timevarying systems. J. Math. Systems Estim. Control 5 (1995), 123-126
22. Descusse, J. and Moog, C. H.: Decoupling with dynamic compensation for strong invertible affine nonlinear systems. Internat. J. Control 42 (1985), 1387-1398
23. Descusse, J. and Moog, C. H.: Dynamic decoupling for right-invertible nonlinear systems. Systems Control Lett. 8 (1987), 345-349
24. Di Benedetto, M.D., Grizzle, J.W. and Moog, C. H.: Rank invariants of nonlinear systems. SIAM J. Control Optim. 27 (1989), 658-672
25. Diop, S.: Elimination in control theory. Math. Control Signals Systems 4 (1991), 17-32
26. El Asmi, S.: An algebraic approach to essentiality. InC. Commault, D. Normand-Cyrot, J.-M. Dion, L. Dugard, M. Fliess, A. Titli, G. Cohen, A. Benveniste, and I.D. Landau, editors, Proc. 1st European Control Conference, pages 468-473, Paris 1991, Hermès
27. El Asmi, S. and Fliess, M.: Formules d'inversion. In B. Bonnard, B. Bride, J-P. Gauthier, and I. Kupka, editors. Controlled Dynamical Systems, volume 8 of Progr. Systems Control Theory, pages 201-210. Birkhäuser, 1991
28. Fliess, M.: Automatique et corps différentiels. Forum Math. 1 (1989), 227-238
29. Fliess, M.: Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Trans. Automat. Control AC-35 (1990), 994-1001
30. Fliess, M.: Some basic structural properties of generalized linear systems. Systems Control Lett. 15 (1990), 391-396
31. Fliess, M. and Glad, S.T.: An algebraic approach to linear and nonlinear control. In H. L. Trentelman and J. C. Willems, editors. Essays on Control: Perspectives in the Theory and its Applications, volume 14 of Progr. Systems Control Theory, pages 223-267, Boston 1993, Birkhäuser
32. Fliess, M., Lévine, J., Martin, P. and Rouchon, P.: Flatness and defect of nonlinear systems: introductory theory and examples. Internat. J. Control 61 (1995), 1327-1361
33. Fliess, M., Lévine, J., Martin, P. and Rouchon, P.: Deux applications de la géométrie locale des diffïétés. Ann. Inst. H. Poincaré Phys. Théor. 66 (1997), 275-232
34. Hartshorne, R.: Algebraic Geometry. Springer Verlag, New York 1977
35. Hilbert, D.: Über den Begriff der Klasse von Differentialgleichungen. Math. Ann. 73 (1913), 95-108
36. Hirschorn, R. M.: Invertibility of multivariable nonlinear control systems. IEEE Trans. Automat. Control AC-24 (1979), 855-865
37. Huijberts, H.J.C., Nijmeijer, H. and van der Wegen, L. L. M.: Dynamic disturbance decoupling for nonlinear systems. SIAM J. Control Optim. 30 (1992), 336-349
38. Isidori, A.: Nonlinear Control Systems. Springer-Verlag, 2nd edition, 1989
39. Jacobson, N.: Basic Algebra, volume I and II. Freeman, New York, second edition, 1985
40. Johnson, J.: Differential dimension polynomials and a fundamental theorem on differential modules. Amer. J. Math. 91 (1969), 239-248
41. Johnson, J.: Kähler differentials and differential algebra. Ann. of Math. 89 (1969), 92-98
42. Johnson, J.: Kahler differentials and differential algebra in arbitrary characteristic. Trans. Amer. Math. Soc. 192 (1974), 201-208
43. Johnson, J.: A notion of regularity for differential local algebra. In H. Bass, P.. Cassidy, and J. Kovacic, editors. Contributions to Algebra (A Collection of Papers Dedicated to Ellis Kolchin), pages 211-232, New York 1977, Academic Press
44. Kolchin, E. R.: Differential Algebra and Algebraic Groups. Academic Press, New York 1973
45. Kunz, E.: Kahler differentials. Vieweg, Braunschweig/Wiesbaden 1986
46. Li, C.-W. and Feng, Y-K.: Functional reproductibility of general multivariable analytic non-linear systems. Internat. J. Control 45 (1987), 255-268
47. Martin, P.: Contribution à l'étude des systèmes différentiellement plats. Thèse de Doctorat, École Nationale Supérieure des Mines de Paris, 1992
48. Martin, P.: Endogenous feedbacks and equivalence. In U. Helmke, R. Mennicken, and J. Saurer, editors. Systems and Networks: Mathematical Theory and Applications (MTNS '93, Volume II, Invited and Contributed Papers), pages 343-346, Berlin 1994, Akademie Verlag
49. Moog, C.H.: Nonlinear decoupling and structure at infinity. Math. Control Signals Systems 1 (1988), 257-268
50. Moog, C. H. and Grizzle, J. W.: Découplage non linéaire vu de l'algèbre linéaire. C. R. Acad. Sei. Paris Sér. I Math. 307 (1988), 497-500
51. Morse, A.S.: Structural invariants of linear multivariable systems. SIAM J. Control 11 (1973), 446-465
52. Nijmeijer, H.: On the theory of nonlinear control systems. In M.Thoma and A. Wyner, editors. Three decades of mathematical system theory, volume 135 of Lecture Notes in Control and Inform. Sci., pages 339-354, Berlin 1989, Springer-Verlag
53. Nijmeijer, H. and Respondek,W.: Dynamic input-output decoupling of nonlinear control systems. IEEE Trans. Automat. Control AC-33 (1988), 1065-1070
54. Nijmeijer, H. and van der Schaft, A. J.: Nonlinear Dynamical Control Systems. Springer-Verlag, New York 1990
55. Nǎstǎsescu, C. and Van Oystaeyen, R: Graded and Filtered Rings and Modules, volume 758 of Lecture Notes in Math. Springer-Verlag, Berlin 1979
56. Perdon, A.M., Conte, G. and Moog, C.H.: Some canonical properties of nonlinear systems. In M. A. Kaashoek, J. H. van Schuppen, and A. C. M. Ran, editors. Realization and Modelling in System Theory (MTNS-89), pages 89-96, Boston 1990, Birkhäuser
57. Perdon, A.M., Zheng, Y.-F., Moog, C.H. and Conte, G.: Disturbance decoupling for nonlinear systems: a unified approach. Kybernetika (Prague) 29 (1993), 479-484
58. Respondek.W.: Disturbance decoupling via dynamic feedback. In B. Bonnard, B. Bride, J.-P. Gauthier, and I. Kupka, editors. Controlled Dynamical Systems, volume 8 of Progr. Systems Control Theory, pages 347-357, Birkhäuser, 1991
59. Respondek,W. and Nijmeijer, H.: On local right-invertibility of nonlinear control systems. Control Theory Adv. Tech. 4 (1988), 325-348
60. Ritt, J. F.: Differential Algebra. American Mathematical Society, New York 1950
61. Rudolph, J.: Viewing input-output system equivalence from differential algebra. J. Math. Systems Estim. Control 4 (1994), 353-383
62. Rudolph, J.: Well-formed dynamics under quasi-static state feedback. In B. Jakubczyk, W. Respondek, and T. Rzeżuchowski, editors, Geometry in Nonlinear Control and Differential Inclusions, volume 32 of Banach Center Publ., pages 349-360, Warszawa 1995
63. Rudolph, J. and Delaleau, E.: Some examples and remarks on quasi-static feedback of generalized states. Submitted
64. Rudolph, J. and Delaleau, E.: Nonlinear right-model matching by proper compensation or quasi-static feedback. In J. W. Nieuwenhuis, C. Praagman, and H. L. Trentelman, editors, Proc. 2nd European Control Conference, pages 1528-1533, 1993
65. Rudolph, J. and Delaleau, E.: Some remarks on quasi-static feedback of generalized states. In Prepr. 1st IFAC Workshop on New Trends in Design of Control Systems, Smolenice, Slovak Republic, pages 47-52, 1994
66. Rudolph, J. and El Asmi, S.: Filtrations and Hilbert polynomials in control theory. In U. Helmke, R. Mennicken, and J. Saurer, editors. Systems and Networks: Mathematical Theory and Applications (MTNS '93, Volume II, Invited and Contributed Papers), pages 449-452, Berlin 1994, Akademie Verlag
67. Seidenberg, A.: Some basic theorem in differential algebra (characteristic p. arbitrary). Trans. Amer. Math. Soc. 73 (1952), 174-190
68. Silverman, L.M.: Inversion of multivariable linear systems. IEEE Trans. Automat. Control AC-14 (1969), 270-276
69. Singh, S.N.: A modified algorithm for invertibility in nonlinear systems. IEEE Trans. Automat. Control AC-26 (1981), 595-598
70. Wonham, W. M.: Linear Multivariable Control: a Geometric Approach. Springer-Verlag, New York, 3rd edition, 1985