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Article

Keywords:
controlled invariance; dynamic state feedback; disturbance decoupling; differential forms
Summary:
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.
References:
[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 10.1137/S0363012994267315 | MR 1416497 | Zbl 0863.93014
[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 10.1109/9.898712 | MR 1809482 | Zbl 1056.93549
[4] Delaleau E., Fliess M.: Algorithme de structure, filtrations et découplage. C. R. Acad. Sci. Paris 315 (1992), Serie I, 101–106 MR 1172415 | Zbl 0791.68113
[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 10.1515/form.1990.2.213 | MR 1050406 | Zbl 0706.93039
[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 10.1109/TAC.1985.1104079 | MR 0799480
[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 10.1137/0331046 | MR 1227545 | Zbl 0785.93036
[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 0925.93412
[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 10.1137/S0363012994277190 | MR 1444345 | Zbl 1047.93526
[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 1167108
[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 1315192 | Zbl 0837.93024
[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 10.1016/S0167-6911(84)80102-4 | MR 0777852 | Zbl 0556.93031
[16] Nijmeijer H., Schaft A. van der: Nonlinear Dynamical Control Systems. Springer-Verlag, Berlin 1990 MR 1047663
[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 1115318 | Zbl 0729.93035
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