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摘要翻译：
在复平面中，一元多项式的频率响应是该多项式沿虚轴求值时所取值的集合。这是一条代数曲线，将平面划分为几个连通的分量。本文证明了包含原点的分量可以用一个线性矩阵不等式精确表示当且仅当多项式是稳定的，在它的所有根都有负实部的意义下。
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英文标题：
《On convexity of the frequency response of a stable polynomial》
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作者：
Didier Henrion (LAAS, Fel-Cvut)
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In the complex plane, the frequency response of a univariate polynomial is the set of values taken by the polynomial when evaluated along the imaginary axis. This is an algebraic curve partitioning the plane into several connected components. In this note it is shown that the component including the origin is exactly representable by a linear matrix inequality if and only if the polynomial is stable, in the sense that all its roots have negative real parts.
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PDF链接：
https://arxiv.org/pdf/0709.1064
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