A Note on the Inversion of Sylvester Matrices in Control Systems. (26th May 2011)

• Record Type: Journal Article
• Authors: Li, Hongkui; Li, Ranran
• Other Names: Milovanović Gradimir V. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2011(2011)
• Publication Date: 2011-05-26
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2011/609863
• Languages: English
• ISSNs: 1024-123X

Abstract

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.