Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 609863, 10 pages
doi:10.1155/2011/609863
Research Article

A Note on the Inversion of Sylvester Matrices in Control Systems

College of Science, Shandong University of Technology, Shandong 255049, China

Received 21 November 2010; Revised 28 February 2011; Accepted 31 March 2011

Academic Editor: Gradimir V. Milovanović

Copyright © 2011 Hongkui Li and Ranran Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.