Bilateral polynomial equations with unimodular right-hand-side matrices

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 4, page 511-514
  • ISSN: 1641-876X

Abstract

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Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.

How to cite

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Kaczorek, Tadeusz. "Bilateral polynomial equations with unimodular right-hand-side matrices." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 511-514. <http://eudml.org/doc/207663>.

@article{Kaczorek2003,
abstract = {Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {bilateral; unimodular procedure; solution; polynomial equation; bilateral polynomial equation; controllability; observability; existence of a solution; computation},
language = {eng},
number = {4},
pages = {511-514},
title = {Bilateral polynomial equations with unimodular right-hand-side matrices},
url = {http://eudml.org/doc/207663},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Bilateral polynomial equations with unimodular right-hand-side matrices
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 511
EP - 514
AB - Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.
LA - eng
KW - bilateral; unimodular procedure; solution; polynomial equation; bilateral polynomial equation; controllability; observability; existence of a solution; computation
UR - http://eudml.org/doc/207663
ER -

References

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  1. Dai L. (1989): Singular Control Systems. - Berlin: Springer. Zbl0669.93034
  2. Delin Chu and D.W.C. Ho (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. (2000a): 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. (2000b): Perfect functional observers of singular continuous-time linear systems. - Mach. Intell. Robot. Contr., Vol. 4, No. 1, pp. 77-82. 
  6. Kaczorek T. (2000c): Polynomial approach to pole shifting to infinity in singular systems by feedbacks. - Bull. Pol. Acad. Techn. Sci., Vol. 50, No. 2, pp. 1340-144. Zbl1038.93037
  7. Kaczorek T. (2003): Relationship between infinite eigenvalue assignment for singular systems and solvability of polynomial matrix equations. -Proc. 11th Mediterranean Conf. Control and Automation MED'03, Rhodes, Greece, (on CD-ROM). Zbl1049.34005
  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. 

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