Abstract
The paper deals with exponential representations for nonlinear discrete-time systems. It is shown how such representations provide a unified framework to study nonlinear discrete-time dynamics as well as sampled dynamics. Bilinear systems are shortly investigated. This paper has been written at the occasion of the 65th birthday of Professor Ruberti who, in the beginning of the 70s, promoted in Italy research activities in nonlinear control starting from bilinear systems.
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References
A. Arapostathis, B. Jakubczyk, H.G. Lee, Marcus and E.D. Contag, The effect of sampling on linear equivalence and feedback linearization, Systems and Cont. Letters, 13, 1989, 373–381.
M. Fliess, Should the theories for continuous-time and discrete-time linear and nonlinear systems really look alike?, in “Nonlinear stems Control Design”, A. Isidori Ed., Pergamon Press, Oxford, 1989.
R. Goodman, Lifting vector fields to nilpotent Lie groups, J. Math. Pures et Appl., 57, 1978, 77–86.
J.W. Grizzle, Feedback linearization of discrete-time systems, Systems and Cont. Letters, 9, 1987, 411–416.
A. Isidori, Nonlinear Control Systems: An Introduction, (II ed.), Springer-Verlag, 1989.
B. JakubczykFeedback linearization of discrete-time systems, Systems and Cont. Letters, 9, 1987, 411–416.
B. Jakubczyk and E.D. Sontag, Controllability of nonlinear discrete time systems; a Lie algebraic approach, SIAM J. Cont. and Opt., 28, 1990.
H.G. Lee, A. Arapostathis and S.I. Marcus, On the linearization of discrete-time systems, Int. J. Cont., 45, 1987, 1783–1785.
S. Monaco and D. Normand-Cyrot, Invariant distributions for discrete-time nonlinear systems, Systems and Cont. Letters, 5, 1985, 191–196.
S. Monaco and D. Normand-Cyrot, Zero dynamics of sampled nonlinear systems, Systems and Cont. Letters, 11, 1988, 229–234.
S. Monaco and D. Normand-Cyrot, Functional expansions for nonlinear discrete-time systems, Math. Sys. Theo., 21, 1989, 235–254.
S. Monaco and D. Normand-Cyrot, A combinatorial approach to the nonlinear sampling problem, in Lect. Notes in Cont. and Info. Sciences, A Bensoussan and J.L. Lions Eds., Vol. 144, Springer-Verlag, 1990, 788–797.
R. Ree, Lie elements and an algebra associated with shuffles, Ann. of Maths., 68, 1958, 210–220.
P. d’Alessandro, A. Isidori and A. Ruberti, Realization and structure theory of bilinear dynamical systems, SIAM J. Cont., 12, 1974, 517–537.
E.D. Sontag, An eigenvalue for sampled weak controllability of billin ear systems, Systems and Cont. Letters, 7, 1986, 313–316.
H.J. Sussmann, Lie brackets, real analycity and geometric control, in “Differential Geometric Control Theory”, R.W. Brond al. Eds., Birkhäuser, 1983, 1–116.
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© 1992 Springer Science+Business Media New York
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Monaco, S., Normand-Cyrot, D. (1992). Canonical Representations of Nonlinear Discrete-time Systems. In: Isidori, A., Tarn, TJ. (eds) Systems, Models and Feedback: Theory and Applications. Progress in Systems and Control Theory, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2204-8_12
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DOI: https://doi.org/10.1007/978-1-4757-2204-8_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-2206-2
Online ISBN: 978-1-4757-2204-8
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