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A generalization of an inequality of Coppel

Author: G. A. Hewer
Journal: Proc. Amer. Math. Soc. 44 (1974), 151-156
MSC: Primary 34A30
MathSciNet review: 0333315
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Abstract: Upper and lower bounds for the solutions of a linear ordinary differential equation are determined from the solutions of upper and lower matrix comparison equations. The coefficients of the comparison equations are computed with the help of Lozinskiĭ's logarithmic ``norm''

$\displaystyle l(A) = \mathop {\lim }\limits_{h \to + 0} [\vert I + hA\vert - 1]/h,$

and the concept of the ``matricial norm'' as a matrix of scalar norms. Using these estimates some new criteria for the stability of composite systems are obtained.

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Keywords: Differential inequalities, positive matrix, matricial and vectorial norms, logarithmic norm
Article copyright: © Copyright 1974 American Mathematical Society