An explicit solution to the matrix equation AV+BW=EV J
Aiguo WU
Guangren DUAN
Bin ZHOU
摘要：In this note,the matrix equation AV+BW=EV J is considered,where E,A and B are given matrices of appropriate dimensions,J is an arbitrarily given Jordan matrix,V and W are the matrices to be determined.Firstly,a right factorization of(sE-A)-1 B is given based on the Leverriver algorithm for descriptor systems.Then based on this factorization and a proposed parametric solution,an alternative parametric solution to this matrix equation is established in terms of the R-controllability matrix of(E,A,B),the generalized symmetric operator and the observability matrix associated with the Jordan matrix J and a free parameter matrix.The proposed results provide great convenience for many analysis and design problems.Moreover,some equivalent forms are proposed.A numerical example is employed to illustrate the effect of the proposed approach.
机标关键词：matrix equationright factorizationsymmetric operatordescriptor systems
分类号：TP3(计算技术、计算机技术)
资助基金：国家杰出青年科学基金(69925308)
论文发表日期：2007-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：6( 47-52 )
英文信息