quotation:		[Copy]
		Bin ZHOU,Guangren DUAN.[en_title][J].Control Theory and Technology,2007,5(4):397~403.[Copy]

This Paper:Browse 834 Download 104	码上扫一扫！

BinZHOU,GuangrenDUAN
0 Fontlarge +\|Default\|Small
()

摘要:

关键词:

DOI：

Received:June 16, 2006Revised:November 22, 2006

基金项目:

Solutions to the generalized Sylvester matrix equations by a singular value decomposition

Bin ZHOU, Guangren DUAN

(Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin Heilongjiang 150001, China)

Abstract:

In this paper, solutions to the generalized Sylvester matrix equations AX-XF=BY and MXN-X=TY with A,M ∈R ,B,T∈R, F,N∈R and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n×(n + pr). The algorithm proposed in this paper for the euqation AX-XF = BY does not require the controllability of matrix pair (A,B) and the restriction that A,F don’t have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.

Key words: Generalize Sylvester matrix equations General solutions Companion matrix Singular value decomposition