eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
The strong Popov form of nonlinear input–output equations; pp. 193–206

Zbigniew Bartosiewicz, Ewa Pawłuszewicz, Małgorzata Wyrwas, Ülle Kotta ORCID Icon, Maris Tõnso

The equivalence transformations are applied to bring a system of nonlinear input–output (i/o) equations into a nonlinear equivalent of the Popov form, called the strong Popov form, under the assumption that the i/o equations already are in the strong row-reduced form.



1. Bartosiewicz, Z., Belikov, J., Kotta, Ü., Tõnso, M., and Wyrwas, M. On the transformation of a nonlinear discrete-time input–output system into the strong row-reduced form. Proc. Estonian Acad. Sci., 2016, 65, 220–236.

2. Bartosiewicz, Z., Kotta, Ü., Pawłuszewicz, E., Tõnso, M., and Wyrwas, M. Transforming a set of nonlinear input-ouput equations into Popov form. In 2015 IEEE 54th Annual Conference on Decision and Control (CDC) : December 15–18, 2015. Osaka, Japan, Proceedings. Piscataway, N.J., 2015, 7131–7136.

3. Beckermann, B., Cheng, H., and Labahn, G. Fraction-free row reduction of matrices of Ore polynomials. J. Symb. Comput., 2006, 41, 513–543.

4. Cheng, H. and Labahn, G. Output-sensitive modular algorithms for polynomial matrix normal forms. J. Symb. Comput., 2007, 42, 733–750.

5. Conte, G., Moog, C. H., and Perdon, A. M. Algebraic Methods for Nonlinear Control Systems. Springer, London, 2007.

6. Davis, P., Cheng, H., and Labahn. G. Computing Popov form of general Ore polynomial matrices. In Proceedings of Milestones in Computer Algebra, Tobago. 2008, 149–156.

7. Farb, B. and Dennis, R. K. Noncommutative Algebra. Springer, New York, 1993.

8. Kojima, C., Rapisarda, P., and Takaba, K. Canonical forms for polynomial and quadratic differential operators. Systems & Control Letters, 2007, 56, 678–684.

9. Kotta, Ü., Bartosiewicz, Z., Nõmm, S., and Pawluszewicz, E. Linear input-output equivalence and row reducedness of discretetime nonlinear systems. IEEE Trans. Autom. Control, 2011, 56, 1421–1426.

10. Middeke, J. A Computational View on Normal Forms of Matrices of Ore Polynomials. PhD thesis, Johannes Kepler University, Linz, 2011.

11. Sriniwas, G. R., Arkun, Y., Chien, I.-L., and Ogunnaike, B. A. Nonlinear identification and control of a high-purity distillation column: a case study. J. Process Control, 1995, 5, 149–162.

12. Van der Schaft, A. J. On realization of nonlinear systems described by higher-order differential equations. Math. Syst. Theory, 1987, 19, 239–275.


Back to Issue