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A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems
Kybernetika, Tome 40 (2004) no. 2, pp. 197-206 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.
The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.
Classification : 58A10, 93B25, 93C10, 93C55
Keywords: controlled invariance; dynamic state feedback; disturbance decoupling; differential forms 
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Aranda-Bricaire, Eduardo; Kotta, Ülle. A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems. Kybernetika, Tome 40 (2004) no. 2, pp. 197-206. http://geodesic.mathdoc.fr/item/KYB_2004_40_2_a2/

[1] Aranda-Bricaire E., Kotta Ü.: Dynamic disturbance decoupling for discrete-time nonlinear systems: a linear algebraic solution. In: Proc. IFAC Conference on System Structure and Control, Nantes, France, July 1995, pp. 155–160

[2] Aranda-Bricaire E., Kotta, Ü., Moog C.: Linearization of discrete-time systems. SIAM J. Control Optim. 34 (1996), 1999–2023 | DOI | MR | Zbl

[3] Aranda-Bricaire E., Kotta Ü.: Generalized controlled invariance for discrete-time nonlinear systems with an application to the dynamic disturbance decoupling problem. IEEE Trans. Automat. Control 46 (2001), 165–171 | DOI | MR | Zbl

[4] Delaleau E., Fliess M.: Algorithme de structure, filtrations et découplage. C. R. Acad. Sci. Paris 315 (1992), Serie I, 101–106 | MR | Zbl

[5] Delaleau E., Fliess M.: An algebraic interpretation of the structure algorithm with an application to feedback decoupling. In: Nonlinear Control Systems Design – Selected Papers from the 2nd IFAC Symposium (M. Fliess, ed.), Pergamon Press, Oxford 1993, pp. 489–494

[6] Fliegner T., Nijmeijer H.: Dynamic disturbance decoupling for nonlinear discrete-time systems. In: Proc. 33rd IEEE Conference on Decision and Control, Buena Vista, Florida 1994, Volume 2, pp. 1790–1791

[7] Fliess M.: Automatique en temps discret et algèbre aux différences. Forum Mathematicum 2 (1990), 213–232 | DOI | MR | Zbl

[8] Grizzle J. W.: Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problem. IEEE Trans. Automat. Control 30 (1985), 868–873 | DOI | MR

[9] Grizzle J. W.: A linear algebraic framework for the analysis of discrete-time nonlinear systems. SIAM J. Control Optim. 31 (1993), 1026–1044 | DOI | MR | Zbl

[10] Huijberts H. J. C., Moog C. H.: Controlled invariance of nonlinear systems: nonexact forms speak louder than exact forms. In: Systems and Networks: Mathematical Theory and Application, Volume II (U. Helmke, R. Mennicken, and J. Saurer, eds.), Akademie Verlag, Berlin 1994, pp. 245–248 | Zbl

[11] Huijberts H. J. C., Moog C. H., Andiarti R.: Generalized controlled invariance for nonlinear systems. SIAM J. Control Optim. 35 (1997), 953–979 | DOI | MR | Zbl

[12] Kotta Ü.: Dynamic disturbance decoupling for discrete-time nonlinear systems: the nonsquare and noninvertible case. Proc. Estonian Academy of Sciences. Phys. Math. 41 (1992), 14–22 | MR

[13] Kotta Ü.: Dynamic disturbance decoupling for discrete-time nonlinear systems: a solution in terms of system invariants. Proc. Estonian Academy of Sciences Phys. Math. 43 (1994), 147–159 | MR | Zbl

[14] Kotta Ü., Nijmeijer H.: Dynamic disturbance decoupling for nonlinear discrete-time systems (in Russian). Proc. Academy of Sciences of USSR,. Technical Cybernetics, 1991, pp. 52–59

[15] Monaco S., Normand-Cyrot D.: Invariant distributions for discrete-time nonlinear systems. Systems Control Lett. 5 (1984), 191–196 | DOI | MR | Zbl

[16] Nijmeijer H., Schaft A. van der: Nonlinear Dynamical Control Systems. Springer-Verlag, Berlin 1990 | MR

[17] Perdon A. M., Conte, G., Moog C. H.: Some canonical properties of nonlinear systems. In: Realization and Modeling in System Theory (M. A. Kaashoek, J. H. van Schuppen, and A. C. M. Ran, eds.), Birkhäuser, Boston 1990, pp. 89–96 | MR | Zbl