# The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 2, page 161-167
- ISSN: 1641-876X

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topKaczorek, Tadeusz. "The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 161-167. <http://eudml.org/doc/207631>.

@article{Kaczorek2003,

abstract = {Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.},

author = {Kaczorek, Tadeusz},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {singular; polynomial matrix equation; infinite eigenvalue; assignment; system; relationship; infinite eigenvalue assignment; descriptor system; perfect observer; state feedback},

language = {eng},

number = {2},

pages = {161-167},

title = {The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations},

url = {http://eudml.org/doc/207631},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Kaczorek, Tadeusz

TI - The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 2

SP - 161

EP - 167

AB - Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.

LA - eng

KW - singular; polynomial matrix equation; infinite eigenvalue; assignment; system; relationship; infinite eigenvalue assignment; descriptor system; perfect observer; state feedback

UR - http://eudml.org/doc/207631

ER -

## References

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- Kaczorek T. (2002a): Perfect functional observers of singular continuous-time linear systems. - Mach. Intell.Robot. Contr., Vol. 4, No. 1, pp. 77-82.
- Kaczorek T. (2002b): Polynomial approach to pole shifting to infinity in singular systems by feedbacks.- Bull. Pol. Acad. Sci. Techn. Sci., Vol. 50, No. 2, pp. 134-144. Zbl1038.93037
- Kaliath T. (1980): Linear Systems. -Englewood Cliffs: Prentice Hall.
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- Kučera V. (1979): Discrete Linear Control, The Polynomial Equation Approach. - Chichester: Wiley. Zbl0432.93001
- Kučera V. (1981): Analysis and Design of Discrete Linear Control Systems. - Prague: Academia.
- Wonham W.M. (1979): Linear Multivariable Control: A Geometric Approach. -New York: Springer. Zbl0424.93001

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