Title :
The subpositive definite solution of the unified algebraic Lyapunov equation over quaternion field
Author_Institution :
Coll. of Math. & Comput. Sci., Guangxi Univ. for Nat., Nanning, China
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;
Conference_Titel :
Control Conference (CCC), 2011 30th Chinese
Conference_Location :
Yantai
Print_ISBN :
978-1-4577-0677-6
Electronic_ISBN :
1934-1768
