Lyapunov-type least-squares problems over symmetric cones
Lyapunov-type least-squares problems over symmetric cones
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DOI：
10.1016/j.laa.2012.06.020
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发表时间：
2012-11
影响因子：
1.1
通讯作者：
Ziyan Luo;N. Xiu;Lingchen Kong
中科院分区：
文献类型：
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作者：
Ziyan Luo;N. Xiu;Lingchen Kong
对称锥上的Lyapunov型最小二乘问题是在欧氏若当代数中求对称锥约束下的Lyapunov方程的最小二乘解，它包含了半正定矩阵锥上的Lyapunov型最小二乘问题作为特例.本文首先详细分析了李雅普诺夫算子在欧氏若当代数中的象。利用这些性质以及对称锥的一些特征，我们建立了Lyapunov型最小二乘问题解存在的一些充要条件.最后，我们研究了最小二乘解的唯一性。
The Lyapunov-type least-squares problem over symmetric cone is to find the least-squares solution of the Lyapunov equation with a constraint of symmetric cone in the Euclidean Jordan algebra, and it contains the Lyapunov-type least-squares problem over cone of semidefinite matrices as a special case. In this paper, we first give a detailed analysis for the image of Lyapunov operator in the Euclidean Jordan algebra. Relying on these properties together with some characterizations of symmetric cone, we then establish some necessary and⧹or sufficient conditions for solution existence of the Lyapunov-type least-squares problem. Finally, we study uniqueness of the least-squares solution.