A Note on the Inversion of Sylvester Matrices in Control Systems

Hongkui Li and Ranran Li

Mathematical Problems in Engineering, 2011, vol. 2011, 1-10

Abstract:

We give a sufficient condition (the solvability of two standard equations) of Sylvester matrix by using the displacement structure of the Sylvester matrix, and, according to the sufficient condition, we derive a new fast algorithm for the inversion of a Sylvester matrix, which can be denoted as a sum of products of two triangular Toeplitz matrices. The stability of the inversion formula for a Sylvester matrix is also considered. The Sylvester matrix is numerically forward stable if it is nonsingular and well conditioned.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:609863

DOI: 10.1155/2011/609863

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