Bilateral polynomial matrix equations in two indeterminates |
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Authors: | Li Xu Osami Saito Kenichi Abe |
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Affiliation: | (1) Toyohashi University of Technology, 441 Tempaku Toyohashi Aichi, Japan |
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Abstract: | Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -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 -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. |
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Keywords: | Polynomial matrices Bilateral equations 2-D systems 2-D polynomial skew primeness |
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