Unified Parametrization for the Solutions to the Polynomial Diophantine Matrix Equation and the Generalized Sylvester Matrix Equation

作者：Zhou Bin^*; Yan Zhi Bin; Duan Guang Ren

来源：International Journal of Control Automation and Systems, 2010, 8(1): 29-35.

DOI：10.1007/s12555-010-0104-0

• Coprime factorization and Bezout identity
• Diophantine matrix equation
• generalized Sylvester mapping
• generalized Sylvester matrix equation
• linear system theory
• parametrization

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.

• 出版日期2010-2
• 单位哈尔滨工业大学