Well-formed dynamics under quasi-static state feedback
Banach Center Publications (1995)
- Volume: 32, Issue: 1, page 349-360
- ISSN: 0137-6934
Access Full Article
topAbstract
topHow to cite
topRudolph, J.. "Well-formed dynamics under quasi-static state feedback." Banach Center Publications 32.1 (1995): 349-360. <http://eudml.org/doc/262627>.
@article{Rudolph1995,
abstract = {Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.},
author = {Rudolph, J.},
journal = {Banach Center Publications},
keywords = {flat; linear controllable; quasi-static state feedback},
language = {eng},
number = {1},
pages = {349-360},
title = {Well-formed dynamics under quasi-static state feedback},
url = {http://eudml.org/doc/262627},
volume = {32},
year = {1995},
}
TY - JOUR
AU - Rudolph, J.
TI - Well-formed dynamics under quasi-static state feedback
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 349
EP - 360
AB - Well-formed dynamics are a generalization of classical dynamics, to which they are equivalent by a quasi-static state feedback. In case such a dynamics is flat, i.e., equivalent by an endogenous feedback to a linear controllable dynamics, there exists a Brunovský type canonical form with respect to a quasi-static state feedback.
LA - eng
KW - flat; linear controllable; quasi-static state feedback
UR - http://eudml.org/doc/262627
ER -
References
top- [1] R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, 1965.
- [2] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969.
- [3] P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 173-187. Zbl0199.48202
- [4] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim. 29 (1991), 38-57. Zbl0739.93021
- [5] P. M. Cohn, Free Rings and their Relations, 2nd edition, Academic Press, London, 1985. Zbl0659.16001
- [6] E. Delaleau, Lowering orders of input derivatives in generalized state representations of nonlinear systems, in: Proc. IFAC-Symposium NOLCOS'92, Bordeaux, M. Fliess (ed.), 1992, 209-213.
- [7] E. Delaleau et M. Fliess, Algorithme de structure, filtrations et découplage, C. R. Acad. Sci. Paris Sér. I 315 (1992), 101-106. Zbl0791.68113
- [8] E. Delaleau and W. Respondek, Lowering the orders of derivatives of controls in generalized state space systems, J. Math. Systems Estim. Control, to appear. Zbl0852.93016
- [9] M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238. Zbl0701.93048
- [10] M. Fliess, Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Automat. Control 35 (1990), 994-1001. Zbl0724.93010
- [11] M. Fliess, Some basic structural properties of generalized linear systems, Systems Control Lett. 15 (1990), 391-396. Zbl0727.93024
- [12] M. Fliess, Some remarks on a new characterization of linear controllability, in: Prepr. 2nd IFAC Workshop ``System Structure and Control'', Prague, Sept. 1992, 8-11.
- [13] M. Fliess, Some remarks on the Brunovský canonical form, Kybernetika 29 (1993), 417-422. Zbl0806.93007
- [14] M. Fliess, J. Lévine, P. Martin et P. Rouchon, Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sci. Paris Sér. I 315 (1992), 619-624. Zbl0776.93038
- [15] S. T. Glad, Nonlinear state space and input output descriptions using differential polynomials, in: New Trends in Nonlinear Control Theory, J. Descusse, M. Fliess, A. Isidori and D. Leborgne (eds.), Lecture Notes Control Inform. Sci. 122, Springer, 1988, 182-189.
- [16] A. Isidori, Nonlinear Control Systems: An Introduction, Springer, New York, 1989.
- [17] B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint. Zbl0712.93027
- [18] J. Johnson, Differential dimension polynomials and a fundamental theorem on differential modules, Amer. J. Math. 91 (1969), 239-248. Zbl0179.34303
- [19] J. Johnson, Kähler differentials and differential algebra, Ann. of Math. 89 (1969), 92-98. Zbl0179.34302
- [20] E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973. Zbl0264.12102
- [21] A. Krener, Normal forms for linear and nonlinear systems, Contemp. Math. 68 (1987), 157-189.
- [22] S. Lang, Algebra, Addison-Wesley, Reading, 1971.
- [23] P. Martin, Contribution à l'étude des systèmes différentiellement plats, Thèse, Ecole des Mines de Paris, 1992.
- [24] H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems, Springer, New York, 1990. Zbl0701.93001
- [25] J. B. Pomet, C. H. Moog, and A. Aranda, A non-exact Brunovský form and dynamic feedback linearization, in: Proc. 31st CDC IEEE, Tucson, 1992, 2012-2017.
- [26] J. F. Ritt, Differential Algebra, Amer. Math. Soc., New York, 1950.
- [27] P. Rouchon, Necessary condition and genericity of dynamic feedback linearization, J. Math. Systems Estim. Control 4 (1994), 1-14. Zbl0818.93012
- [28] J. Rudolph, Une forme canonique en bouclage quasi statique, C. R. Acad. Sci. Paris Sér. I 316 (1993), 1323-1328.
- [29] J. Rudolph, A canonical form under quasi-static feedback, in: Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer (eds.), 1993, 445-448. Zbl0925.93107
- [30] J. Rudolph, Viewing input-output system equivalence from differential algebra, J. Math. Systems Estim. Control 4 (1994), 353-383. Zbl0806.93012
- [31] J. Rudolph, Duality in time-varying linear systems: a module theoretic approach, Linear Algebra Appl., to appear. Zbl0864.93035
- [32] J. Rudolph and S. El Asmi, Filtrations and Hilbert polynomials in control theory, in: Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Saurer (eds.), 1994, 449-452. Zbl0925.93133
- [33] W. Sluis, Absolute Equivalence and its Applications to Control Theory, PhD Thesis, University of Waterloo, 1992.
- [34] M. Zeitz, Canonical forms for nonlinear systems, in: Nonlinear Control Systems Design, Selected Papers from the IFAC-Symposium, Capri/Italy 1989, A. Isidori (ed.), Pergamon Press, Oxford, 1990, 33-38.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.