发表机构
Université de Lorraine; University of Melbourne（洛林大学; 墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过从子集和问题到无约束静态输出反馈镇定的多项式时间归约，证明了该镇定问题的NP困难性，并利用频率分离和根数比较给出了显式增益界。
AI 中文摘要
本文给出了从子集和问题到无约束静态输出反馈镇定的多项式时间归约，确立了其NP困难性。该构造使用两个标量构建块来施加近似离散选择和加权和约束。一旦问题被编码，我们将编码问题的$N+1$个解耦回路的稳定性与耦合被控对象的稳定性联系起来。这是通过利用带通变换进行频率分离，并比较真实特征多项式与不同块在右半平面不同区域中的根数来实现的。该构造自然地界定了每个镇定增益，并给出了显式的模量裕度估计，确保被控对象数据具有多项式二进制编码长度。
英文摘要
In this paper we give a polynomial-time reduction from the Subset Sum Problem to unconstrained static output feedback stabilization, establishing its NP-hardness. The construction uses two scalar building blocks to impose approximate discrete choices and a weighted-sum constraint. Once the problem is encoded, we relate the stability of the $N+1$ decoupled loops encoding the problem to that of a coupled plant. This is accomplished by leveraging frequency separation via a band-pass transformation, and comparing the root counts of the true characteristic polynomial with that of the different blocks in different regions of the right half-plane. The construction then naturally bounds every stabilizing gain and gives explicit modulus-margin estimates, ensuring that the plant data have polynomial binary encoding length.
