论文标题
在LMI地区表征具有特征值的矩阵
Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach
论文作者
论文摘要
在本文中，我们为特征值属于给定的LMI区域的一组矩阵提供了耗散性的哈密顿（DH）表征。这种特征是Choudhary等人的概括。 （数字线性代数应用，2020）到任何LMI区域。它可以在各种上下文中使用，我们在最接近的$ω$ - 稳定矩阵问题上说明了它：给定LMI区域$ω\ subseteq \ subseteq \ mathbb {c} $和一个矩阵$ a \ in \ mathbb {c}^c}^{c}^{n，n，n，n，n} $，找到$ a $ a $ a $ a $ a $ gues $ gues use $ igie $ c。最后，我们将表征推广到可以使用涉及复杂矩阵的LMI表示的更一般的区域。
In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl., 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest $Ω$-stable matrix problem: given an LMI region $Ω\subseteq \mathbb{C}$ and a matrix $A \in \mathbb{C}^{n,n}$, find the nearest matrix to $A$ whose eigenvalues belong to $Ω$. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices.
