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

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2003)

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

Abstract

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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.

How to cite

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Kaczorek, 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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  1. Dai L. (1989): Singular Control Systems. - Berlin: Springer. Zbl0669.93034
  2. Chu D. and Ho D.W.C. (1999): Infinite eigenvalue assignment for singular systems. - Lin. Alg. Its Applicns., Vol. 298, No. 1, pp. 21-37. Zbl0987.93037
  3. Kaczorek T. (1993): Linear Control Systems, Vols. 1 and 2. - New York: Wiley. Zbl0784.93003
  4. Kaczorek T. (2000): Reduced-order perfect and standard observers for singular continuous-time linear systems. - Mach. Intell. Robot. Contr., Vol. 2, No. 3, pp. 93-98. 
  5. Kaczorek T. (2002a): Perfect functional observers of singular continuous-time linear systems. - Mach. Intell.Robot. Contr., Vol. 4, No. 1, pp. 77-82. 
  6. 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
  7. Kaliath T. (1980): Linear Systems. -Englewood Cliffs: Prentice Hall. 
  8. Kučera V. (1972): A contribution to matrix equations. - IEEE Trans.Automat. Contr., Vol. AC-17, No. 6, pp. 344-347. Zbl0262.93043
  9. Kučera V. (1979): Discrete Linear Control, The Polynomial Equation Approach. - Chichester: Wiley. Zbl0432.93001
  10. Kučera V. (1981): Analysis and Design of Discrete Linear Control Systems. - Prague: Academia. 
  11. Wonham W.M. (1979): Linear Multivariable Control: A Geometric Approach. -New York: Springer. Zbl0424.93001

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