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of the estonian academy of sciences
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Feedback linearization of discrete-time nonlinear control systems: computational aspects; pp. 11–26
PDF | 10.3176/proc.2020.1.03

Tanel Mullari, Ülle Kotta ORCID Icon

An alternative solution of the static state feedback linearization problem for the discrete-time case is given. This solution is based on the sequence of distributions, whose computation requires only the knowledge of the backward shift equations. This computational method is especially suitable for the class of discrete-time systems, obtained from the implicit Euler discretization of continuous-time systems. As a practical example the implicit Euler discretization of hydraulic press equations is considered. 



1. Jakubczyk, B. Feedback linearization of discrete-time systems. Syst. Control Lett., 1987, 9(5), 411–416.

2. Grizzle, W. Feedback linearization of discrete-time systems. Lecture Notes Contr. Inform. Sci., 1986, 83, 273–281.

3. Aranda-Bricaire,E.,Kotta,Ü.,and Moog,C.H. Linearization of discrete-time systems. SIAMJ. Control. Optim., 1996, 34(6), 1999–2023.

4. Califano, C., Monaco, S., and Normand-Cyrot, D. On the problem of feedback linearization. Syst. Control Lett., 1999, 36(1), 61–67.

5. Mullari, T., Kotta, Ü., Bartosiewicz, Z., Pawluszewicz, E., and Moog, C. H. Forward and backward shifts of vector fields: towards the dual algebraic framework. IEEE Trans. Autom. Control, 2017, 62(6) 3029–3033.

6. Mullari, T. and Schlacher, K. Geometric control for a nonlinear sampled data system. In MTNS 2014: 21st International Symposium of Mathematical Theory of Networks and Systems, July 7–11, 2014, Groningen, the Netherlands, Proceedings. University of Groningen, Groningen, 2014, 54–61.

7. Nam, K. Linearization of discrete-time nonlinear systems and a canonical structure. IEEE Trans. Autom. Control, 1989, 34, 119–211.

8. Jayaraman, G. and Chizek, H. J. Feedback linearization of discrete-time systems. In Proceedings of the 32nd IEEE CDC. San Antonio, 1993, 2972–2977.

9. Kotta, Ü., Tõnso, M., Shumsky, A. Y., and Zhirabok, Z. N. Feedback linearization and lattice theory. Syst. Control Lett., 2013, 62(3), 248–255.

10. Simões, C. and Nijmeijer, H. Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems. Int. J. Robust Nonlinear Control, 1996, 6(3), 171–188.<171::AID-RNC140>3.0.CO;2-0

11. Kaldmäe, A., Kotta,Ü., Shumsky,A.,and Zhirabok, A. Feedback linearization of possible non-smooth systems. Proc. Estonian Acad. Sci., 2017, 66(2), 109–123.

12. Efimov, D., Polyakov, A., Levant, A., and Perruquetti, W. Realization and discretization of asymptotically stable homogenous systems. IEEE Trans. Autom. Control, 2017, 62(11), 5962–5969.

13. Belikov, J., Kaldmäe, A., and Kotta, Ü. Global linearization approach to nonlinear control systems: a brief tutorial overview. Proc. Estonian Acad. Sci., 2017, 66(3), 243–263.

14. Kotta, Ü. Discrete-time models of a nonlinear continuous-time system. Proc. Estonian Acad. Sci. Phys. Math., 1994, 43(1), 64–78.

15. Kotta, Ü., Liu, P., and Zinober, A. S. I. Transfer equivalence and realization of nonlinear higher order i/o difference equations using Maple. In Proceedings of the 4th IFAC World Congress, Vol. E (Chen, H.-F. et al., eds). Pergamon, Beijing, Oxford, 1999, 249–254.


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