Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized Sylvester matrix equation |
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Authors: | Bin Zhou Zhi-Bin Yan Guang-Ren Duan |
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Affiliation: | 1.Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin, Heilongjiang,P. R. China;2.Natural Science Research Center,Harbin Institute of Technology,Harbin, Heilongjiang,P. R. China |
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Abstract: | The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design
in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized
Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present
in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is
shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation
are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester
matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system
theory. |
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Keywords: | |
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