Multidimensional Systems and Signal Processing

, Volume 1, Issue 4, pp 363–379 | Cite as

Bilateral polynomial matrix equations in two indeterminates

  • Li Xu
  • Osami Saito
  • Kenichi Abe


Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=αI withα being a Ω-stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal Ω-stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.


Polynomial matrices Bilateral equations 2-D systems 2-D polynomial skew primeness 


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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Li Xu
    • 1
  • Osami Saito
    • 1
  • Kenichi Abe
    • 1
  1. 1.Toyohashi University of TechnologyTempaku Toyohashi AichiJapan

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