Bilateral polynomial matrix equations in two indeterminates
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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.
KeywordsPolynomial matrices Bilateral equations 2-D systems 2-D polynomial skew primeness
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