The subpositive definite solution of the unified algebraic Lyapunov equation over quaternion field

Author

Huang Jing-pin

Author_Institution

Coll. of Math. & Comput. Sci., Guangxi Univ. for Nat., Nanning, China

fYear

2011

fDate

22-24 July 2011

Firstpage

142

Lastpage

146

Abstract

By using the structure-preserving property of complexification operator of the quaternion matrices, some necessary and sufficient conditions for the existence of subpositive definite solution of the unified algebraic Lyapunov equation A*X+XA+θA*XA = -Q over quaternion field are derived. At the same time, we construct iterative algorithm to find subpositive definite solution of this matrix equation, the convergence of the iteration is analyzed, and the method for selecting sampling period is given. Finally, a numeral example shows the feasibility of the method.

Keywords

Lyapunov matrix equations; convergence of numerical methods; iterative methods; complexification operator; iteration convergence; iterative algorithm; quaternion field; quaternion matrices; structure-preserving property; subpositive definite solution; unified algebraic Lyapunov equation; Eigenvalues and eigenfunctions; Equations; Iterative methods; Mathematical model; Matrix decomposition; Presses; Quaternions; Iterative; Quaternion Field; Sampling Period; Subpositive Definite Solution; Unified Algebraic Lyapunov Equation;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (CCC), 2011 30th Chinese

Conference_Location

Yantai

ISSN

1934-1768

Print_ISBN

978-1-4577-0677-6

Electronic_ISBN

1934-1768

Type

conf

Filename

6001013