论文标题
无限LMI区域中广义D稳定性的问题
The problem of generalized D-stability in unbounded LMI regions
论文作者
论文摘要
我们概括了矩阵的D稳定性和添加剂D稳定性的概念。为此，我们考虑一个根据线性基质不平等（所谓的LMI区域）定义的无限区域的家族。我们研究了当矩阵光谱在未结合的LMI区域中的定位在初始矩阵的特定乘法和加性扰动下保存时。考虑到无限的LMI区域（即圆锥形部门和移动的半平面）的最著名的病例。分析了新的D稳定性标准以及足够的通用D稳定性条件。显示了开发理论对动态系统的几种应用。
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.
