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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Popov form and the explicit equations of inverse systems; pp. 342–355

(Full article in PDF format) https://doi.org/10.3176/proc.2018.4.04


Authors

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

Abstract

The paper addresses the invertibility problem for discrete-time nonlinear control systems, described by the input–output equations. The necessary and sufficient conditions for the existence of left and right inverse systems are given. The explicit equations of inverse systems are found by transforming the system equations into the strong Popov form with respect to inputs. The results are obtained under the assumption that the equations are transformable into the strong Popov form using linear equivalence transformations over the field of meromorphic functions.

Keywords

discrete-time systems, nonlinear systems, input–output models, non-commutative polynomials, strong Popov form.

References

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.
https://doi.org/10.3176/proc.2016.3.02

2. Bartosiewicz , Z. , Kotta , Ü. , Pawłuszewicz , E. , Tõnso , M. , and Wyrwas , M. The strong Popov form of nonlinear input–output equations. Proc. Estonian Acad. Sci. , 2018 , 67 , 193–206.
https://doi.org/10.3176/proc.2018.3.01

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

 
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Current Issue: Vol. 68, Issue 1, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December