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A Note on Recursive Schur Complements, Block Hurwitz Stability of Metzler Matrices, and Related Results

机译:关于递归Schur补码,Metzler矩阵的Block Hurwitz稳定性及相关结果的注记

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摘要

It is known that the stability of a Metzler matrix can be characterized in a Routh–Hurwitz-like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly therefrom using only elementary results from linear algebra. Implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system-theoretic applications of this observation.
机译:众所周知,基于标量Schur补码的递归应用,可以以类似于Routh-Hurwitz的方式来表征Metzler矩阵的稳定性[1]。我们在本简要说明中的目的是表明,最近获得的稳定性条件是该结果的等价陈述,并且可以仅使用线性代数的基本结果直接从中推导得出。还讨论了这种等效性的含义,并给出了几个示例来说明此观察结果的潜在有趣的系统理论应用。

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