Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 21078, 16 pages
On the Parametric Solution to the Second-Order Sylvester Matrix Equation
1Department of Control Engineering, Academy of Armored Force Engineering, Beijing 100072, China
2Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China
Received 30 November 2005; Revised 27 June 2007; Accepted 5 September 2007
Academic Editor: P. T. Kabamba
Copyright © 2007 Wang Guo-Sheng et al. 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.
This paper considers the solution to a class of the second-order Sylvester matrix equation . Under the controllability of the matrix triple , a complete, general, and explicit parametric solution to the second-order Sylvester
matrix equation, with the matrix
in a diagonal form, is proposed. The results provide great convenience to the analysis
of the solution to the second-order Sylvester matrix equation, and can perform important functions in
many analysis and design problems in control systems theory. As a demonstration, an illustrative example
is given to show the effectiveness of the proposed solution.