We generalize the concepts of D-stability and additive D-stability of matrices. For this, we consider a family of unbounded regions defined in terms of Linear Matrix Inequalities (so-called LMI regions). We study the problem when the localization of a matrix spectrum in an unbounded LMI region is preserved under specific multiplicative and additive perturbations of the initial matrix. The most well-known particular cases of unbounded LMI regions (namely, conic sectors and shifted halfplanes) are considered. A new D-stability criterion as well as sufficient conditions for generalized D-stability are analyzed. Several applications of the developed theory to dynamical systems are shown.

我们概括了矩阵的D-稳定性和加性D-稳定性的概念。为此，我们考虑根据线性矩阵不等式定义的一系列无边界区域（所谓的LMI区域）。我们研究在初始矩阵的特定乘法和加法扰动下保留无界LMI区域中的矩阵谱的局部化时的问题。考虑了无界LMI区域（即圆锥形扇区和移动的半平面）的最著名的特殊情况。分析了新的D稳定性准则以及广义D稳定性的充分条件。显示了发达理论在动力系统中的几种应用。