Paper Info
Title
Solution to second-order nonhomogeneous generalized Sylvester equations
Abstract
In this paper, a new type of nonhomogeneous second-order generalized Sylvester equations (GSEs) are proposed. A complete general parametric solution in a neat explicit closed form is established using the F-coprimeness condition. The primary feature of this solution is that the matrix F does not need to be in any canonical form, or may be even unknown a priori. The matrix R, together with the matrix F, may be both set undetermined and used as degrees of freedom beyond the completely free parameter matrix Z. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many control systems analysis and design problems involving second-order dynamical systems.
Year
DOI
Venue
2013
10.1109/ASCC.2013.6606408
ASCC
Keywords
Field
DocType
generalized sylvester equations,f-coprimeness,degree of freedom,control system synthesis,second-order dynamical systems,matrix algebra,gses,completely free parameter matrix z,control system design problem,control system analysis,general parametric solution,matrix r,smith form reduction,matrix f,second-order nonhomogeneous generalized sylvester equations,general solutions,f-coprimeness condition,control systems,linear systems,polynomials,nickel
Applied mathematics,Combinatorics,Sylvester equation,Matrix (mathematics),Canonical form,Dynamical systems theory,Sylvester's law of inertia,State-transition matrix,Sylvester matrix,Mathematics,Free parameter
Conference
Volume
Issue
ISSN
null
null
null
ISBN
Citations 
PageRank 
978-1-4673-5767-8
0
0.34
References 
Authors
2
1
Name
Order
Citations
PageRank
Guang-Ren Duan11735177.31