摘要
利用四元数矩阵的复表示算子,讨论了四元数体上混合Lyapunov方程AX+XA*+BX B*=-F存在唯一亚正定解的必要和充分条件;同时,在方程存在唯一亚正定解的条件下,给出了方程的参数迭代算法并通过数值算例检验了所给方法的可行性.
By using the complexification operator of the quaternion matrices,the necessary and sufficient conditions for the existence of sub-positive definite solution of the mixed-type Lyapunov equation AX＋XA＊＋BXB＊=-F is discussed.At the same time,an iterative algorithm with parameter for solving the equation is proposed,and subpositive definite solution of the equation is obtained by choosing appropriate parameters.Finally,a numerical example indicated the feasibility of the method.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第5期41-46,共6页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
新疆高校科研基金(XJEDU2008I31)
关键词
四元数体
混合Lyapunov方程
亚正定解
参数迭代
quaternion field
mixed-type Lyapunov equation
subpositive definite solution
parameter iterative
