The roles of Sylvester and Bezoutian matrices in the historical study of stability of linear discrete-time systems
The roles of Sylvester and Bezoutian matrices in the historical study of stability of linear discrete-time systems
复制标题
西尔维斯特矩阵和贝祖矩阵在线性离散时间系统稳定性历史研究中的作用
DOI：
10.1109/81.736557
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发表时间：
1998
影响因子：
5.1
通讯作者：
E. Jury
中科院分区：
文献类型：
--
作者：
E. Jury
本文回顾了线性离散时间系统稳定性判据的历史。在这篇评论中，埃尔米特，舒尔，科恩和藤原的早期开创性工作，以及这些工作如何为其他标准的现代发展铺平了道路。西尔维斯特矩阵和Bezoutian矩阵是这类发展的关键方法。除了对早期工作的回顾外，还揭示了一些新的结果和简化。本文最后介绍了各种稳定性判据在不同领域中的一些重要应用。
In this paper, a historical review of the stability criteria of linear discrete-time systems is presented. In this review the early pioneering works of Hermite, Schur, Cohn, and Fujiwara, and how these paved the way for modern development of other criteria are indicated. It is also mentioned that Sylvester and Bezoutian matrices are the key methods in such developments. Besides this review of early work, some new results and simplifications are brought to light. The paper ends with some important applications of the various stability criteria in diverse fields.