In this paper, we introduce the class of diagonally dominant with respect to a given LMI region $\mathfrak{D}\subset \mathbb{C}$ matrices. They are shown to possess the analogues of well-known properties of (classical) diagonally dominant matrices, e.g. their spectra are localized inside the region $\mathfrak{D}$. Moreover, we show that in some cases, diagonal $\mathfrak{D}$-dominance implies $(\mathfrak{D},\mathcal{D})$-stability (i.e. the preservation of matrix spectra localization under multiplication by a positive diagonal matrix).

中文翻译：

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对角优势概念的推广与矩阵 D 稳定性的应用

在本文中，我们介绍了相对于给定 LMI 区域的对角占优类 $\mathfrak{D}\subset \mathbb{丙}$矩阵。它们被证明具有（经典）对角主导矩阵的众所周知的特性的类似物，例如它们的光谱位于该区域内$\mathfrak{D}$. 此外，我们表明，在某些情况下，对角线$\mathfrak{D}$-支配意味着 $(\mathfrak{D},\mathcal{D})$-稳定性（即在乘以正对角矩阵的情况下保留矩阵光谱定位）。