线性系统的同时的稳定是在系统和控制理论的一个基本问题,并且具有理论、实际的意义。在这篇论文,作者在单个输入的单个产量的线性时间不变的系统的同时的稳定上考察最近的研究进步和 state-of-art 结果。特别,作者在从数学理论分析和数字计算的观点涉及众所周知的法语的香槟问题和比利时的巧克力问题的参数上列出曾经最好的结果。并且作者观察到波士顿宣称罐头的更低的界限在 2012 被扩大到 0.976461 不是精确的。作者希望它将在几个线性系统的同时的稳定上启发进一步的学习。
Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known "French Champagne Problem" and "Belgian Chocolate Problem" from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of 5 can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.