Geometric properties of a class of nonlinear discrete-time dynamics

ECC 1997 - European Control Conference

Volumn , Issue , 1997, Pages 3176-3181

  Monaco, S ^a   Normand Cyrot, D ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CNRS   (France)

Author keywords

Differential geometry; Nonlinear discrete time dynamics

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICS; GEOMETRY;

AFFINE SYSTEMS; ANALYSIS PROBLEMS; CONTINUOUS-TIME; DIFFERENTIAL GEOMETRY; DISCRETE TIME DYNAMICS; GEOMETRIC PROPERTIES; NONLINEAR DISCRETE-TIME; SYSTEM OF DIFFERENTIAL EQUATIONS;

CONTINUOUS TIME SYSTEMS;

EID: 84949087689     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.1997.7082599     Document Type: Conference Paper

References (17)

1. F. Albertini and E. D. Sontag, Discrete-time transitivity and accessibility: analytic systems, SIAM J. on Cont. and Opt., vol. 31, 6, 1993, 1599-1622.
2. M. Fliess, Automatique en temps discret et algèbre aux différences, Forum Math, 2, 1990, 213-232.
3. J. W. Grizzle, Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problem, Trans. on Aut. Cont., AC-30, 1985, 868-874.
4. J. W. Grizzle, Feedback linearization of discrete-time systems, Lect. Notes in cont. and Info. Sciences, New York, Springer Verlag, 1986, 273-281.
5. R. Hermann and A. J. Krener, Nonlinear controllability and observability, IEEE Trans. on A. C, AC 22, 1977, 720-740.
6. A. Isidori, Nonlinear Control Systems, (IIIe ed.), Springer-Verlag, 1994.
7. B. Jakubczyk and D. Normand-Cyrot, Orbites des pseudogroupes des difféomorphismes et commandabilite des systemes nonlineaires en temps discret, C R. Acad. Sc. Paris, 298, 11, 1984, 257-260.
8. B. Jakubczyk, Feedback linearization of discretetime systems, Systems and Cont. Letters, 9, 1987, 441-446.
9. B. Jakubczyk and E. D. Sontag, Controllability of nonlinear discrete-time systems; a Lie algebraic approach, SIAM J. Cont. and Opt, 28, 1990.
10. H. G. Lee, A. Arapostathis and S. I. Marcus, Linearization of discrete-time systems, Int. J. Cont., 45, 1986, 1803-1822.
11. C. Lobry, Controllability of nonlinear systems on compact manifolds, SIAM J. on Control, 1974.
12. S. Monaco and D. Normand-Cyrot, Invariant distributions for discrete-time nonlinear systems, Systems and Cont. Letters, 5, 1985, 191-196.
13. S. Monaco and D. Normand-Cyrot, On the sampling of a linear control system, Proc. 24th IEEE-CDC, Fort Lauderdale, USA, 1985, 1457-1462.
14. S. Monaco and D. Normand-Cyrot, Functional expansions for nonlinear discrete-time systems, Math. Sys. Theo., 21, 1989, 235-254.
15. S. Monaco and D. Normand-Cyrot, A unifying representation for nonlinear discrete-time and sampled dynamics, Journal of Mathematic Systems, Estimation and Control, to appear, (summary), 1995, 101-103.
16. R. Ree, Lie elements and an algebra associated with shuffles, Ann. of Maths., 68, 1958, 210-220.
17. H. J. Sussmann, Lie brackets, real analycity and geometric control, Differential Geometric Control Theory, R. W. Brond et al. Eds., Birkhäuser, 1983, 1-116.