ESTONIAN ACADEMY
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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 (2020): 1.045
Transformation of nonlinear discrete-time state equations into the observer form: extension to non-reversible case; pp. 235–247
PDF | 10.3176/proc.2021.3.03

Authors
Tanel Mullari, Ülle Kotta
Abstract

This paper addresses the equivalence under state transformation of a discrete-time nonlinear control system to observer canonical form. Necessary and sufficient conditions for generic equivalence are given for the case when the state equations are not necessarily reversible. The proof is constructive and shows how to find the state transformation if the conditions are satisfied. The derived conditions are then compared with earlier conditions, obtained under more restrictive assumptions, to demonstrate that the earlier result follows directly from our theory. Two examples illustrate the new theory.

References

1. Kaparin, V. and Kotta, Ü. Transformation of nonlinear discrete-time system into the extended observer form. Int. J. Control, 2018, 91(4), 848–858. 
https://doi.org/10.1080/00207179.2017.1294264

2. Lee, H.-G., Arapostathis, A. and Marcus, S. I. Necessary and sufficient conditions for state equivalence to a nonlinear discrete-time observer canonical form. IEEE Trans. Autom. Control, 2008, 53(11), 2701–2707. 
https://doi.org/10.1109/TAC.2008.2008321

3. Lee, H.-G. and Hong, J.-M. Algebraic conditions for state equivalence to a discrete-time nonlinear observer canonical form. Syst. Control Lett., 2011, 60(9), 756–762. 
https://doi.org/10.1016/j.sysconle.2011.06.001

4. Mullari, T. and Kotta, Ü. Transformation the nonlinear system into the observer form: simplifications and extension. Eur. J. Control, 2009, 15(2), 177–183. 
https://doi.org/10.3166/ejc.15.177-183

5. Lee, H. G. Verifiable conditions for discrete-time multi output observer error linearizability. IEEE Trans. Autom. Control, 2019, 64(4), 1632–1639. 
https://doi.org/10.1109/TAC.2018.2850285

6. Califano, C., Monaco, S. and Normand-Cyrot, D. Canonical observer forms for multi-output systems up to coordinate and output transformations in discrete time. Automatica, 2009, 45(11), 2483–2490. 
https://doi.org/10.1016/j.automatica.2009.07.003

7. Califano, C., Monaco, S. and Normand-Cyrot, D. On the observer design in discrete-time. Syst. Control Lett., 2003, 49(4), 255–265. 

8. 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. 
https://doi.org/10.1109/TAC.2016.2608718

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

10. Mullari, T. and Kotta, Ü. Linearization of discrete-time control systems by state transformation. Proc. Est. Acad. Sci., 2021, 70(1), 62–79. 

11. Kotta, Ü., Schlacher, K. and Tõnso, M. Relaxing realizability conditions for discrete-time nonlinear systems. Automatica, 2015, 58, 67–71. 
https://doi.org/10.1016/j.automatica.2015.05.007

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