Paper Info
Title
Solutions to the matrix equation X − AXB = CY+R and its application:
Abstract
The solution of the nonhomogeneous Yakubovich matrix equation X-AXB = CY + R is important in stability analysis and controller design in linear systems. The nonhomogeneous Yakubovich matrix equation X-AXB = CY + R, which contains the well-known Kalman-Yakubovich matrix equation and the general discrete Lyapunov matrix equation as special cases, is investigated in this paper. Closed-form solutions to the nonhomogeneous Yakubovich matrix equation are presented using the Smith normal form reduction. Its equivalent form is provided. Compared with the existing method, the method presented in this paper has no limit to the dimensions of an unknown matrix. The present method is suitable for any unknown matrix, not only low-dimensional unknown matrices, but also high-dimensional unknown matrices. As an application, parametric pole assignment for descriptor linear systems by PD feedback is considered.
Year
DOI
Venue
2018
10.1177/0142331216673422
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
Keywords
DocType
Volume
Nonhomogeneous Yakubovich matrix equation,closed-form solution,Smith normal form reduction
Journal
40.0
Issue
ISSN
Citations 
3
0142-3312
1
PageRank 
References 
Authors
0.35
10
2
Name
Order
Citations
PageRank
Caiqin Song111.03
Guoliang Chen230546.48