ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Linearization of discrete-time control system by state transformation; pp. 62–79
PDF | 10.3176/proc.2021.1.09 | Erratum

Authors
Tanel Mullari, Ülle Kotta ORCID Icon
Abstract

This paper presents necessary and sufficient linearizability conditions by state transformation for discrete-time multi-input nonlinear control system under the mild assumption on the surjectivity property and describes how to find the state transformation when it exists. The conditions are formulated in terms of backward shifts of vector fields, defined by the system dynamics. The conditions are compared with those that allow additionally the regular static state feedback. The theory is illustrated by two examples. 

References

1. 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. Automat. Contr., 2017, 62(6), 3029–3033.
https://doi.org/10.1109/TAC.2016.2608718

2. Aranda-Bricaire, E., Kotta, Ü., and Moog, C. H. Linearization of discrete-time systems. SIAM J. Control Optim., 1996, 34(6), 1999–2023.
https://doi.org/10.1137/S0363012994267315

3. 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.
https://doi.org/10.3176/proc.2017.3.01

4. Lee, A. G., Arapostathis, A., and Marcus, S. I. Linearization of discrete-time systems. Int. J. Control, 1987, 45(5), 1803–1822.
https://doi.org/10.1080/00207178708933847

5. Grizzle, J. V. Feedback linearization of discrete-time systems. Lect. Notes Control Inf. Sci., 1986, 83, 273–281.
https://doi.org/10.1007/BFb0007564

6. Nam, K. Linearization of discrete-time systems and a canonical structure. IEEE Trans. Automat. Contr., 1989, 34(1), 119–122.
https://doi.org/10.1109/9.8665

7. Conte, G., Moog, C. H., and Perdon, A. M. Nonlinear Control Systems: an Algebraic Setting. Springer, London, 1999.

8. Nijmeijer, H. and van der Schaft, A. J. Nonlinear Dynamical Control Systems, Springer, New York, 1990.
https://doi.org/10.1007/978-1-4757-2101-0

9. Kailath, T. Linear Systems, Prentice-Hall, Inc., Upper Saddle River, 1980.

10. Kotta, Ü., Tõnso, M., Shumsky, A., and Zhirabok, A. Feedback linearization and lattice theory. Syst. Control Lett., 2013, 62(3), 248–255.
https://doi.org/10.1016/j.sysconle.2012.11.014

11. Kaldmäe, A., Kotta, Ü., Shumsky, A., and Zhirabok, A. Feedback linearization of possibly non-smooth systems. Proc. Estonian Acad. Sci., 2017, 66(2), 109–123.
https://doi.org/10.3176/proc.2017.2.01

12. Belikov, J., Kaldmäe, A., Kaparin, V., Shumsky, A., Kotta, Ü., Tõnso, M., and Zhirabok, A. Functions’ algebra in nonlinear control: computational aspects and software. Proc. Estonian Acad. Sci., 2017, 66(1), 89–107.
https://doi.org/10.3176/proc.2017.1.06

13. Kotta, Ü. and Mullari, T. Discussion on: ”Unified approach to the problem of full decoupling via output feedback”. Eur. J. Control, 2010, 16(4), 326–328. 
https://doi.org/10.1016/S0947-3580(10)70660-9

14. Kaparin, V. and Kotta, Ü. Transformation of nonlinear MIMO discrete-time systems into the extended observer form. Asian J. Control, 2019, 21(5), 2202–2217.
https://doi.org/10.1002/asjc.1824

Back to Issue