矩阵稳定性的充分条件

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI:10.6028/JRES.078B.015

Charles R. Johnson

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引用次数: 4

摘要

一个n × n的复矩阵x A是正稳定的，如果对于A的每一个e值A, Re (A) > 0。如果A同时满足以下两个条件，则n A是正稳定的:(1)对于每一个k = 1，…。， n, A的k × k的和的实部是正的;(2) A的特征值的所有部分的最小值是A的特征值的最小值。特殊情况包括hermiti A和正有限矩阵和m -矩阵。

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A sufficient condition for matrix stability

An n by n complex matri x A is said to be pos itive stable if Re (A) > 0 for each e igenvalue A of A. If A sati sfies both of the followin g two conditions, the n A is positive stable: (1) for each k = 1, .. . , n , the real part of the sum of the k by k princ ipal minors of A is positive ; and (2) the minimum of the rea l parts of the e igenvalues of A is it se lf an eigenvalue of A. Special cases inc lude hermiti a n positive d e fi nite matrices and M-matrices.

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Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences

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