IJPAM: Volume 115, No. 3 (2017)

Title

SOME INVERSE RESULTS ABOUT MATRIX STABILITY
IN TERMS OF MATRIX MEASURE

Authors

Hristo Kiskinov$^1$, Nedelcho Milev$^2$, Andrey Zahariev$^3$
$^{1,2,3}$Faculty of Mathematics and Informatics
University of Plovdiv
4 Tzar Asen, 4000 Plovdiv, BULGARIA

Abstract

The aim of the present work is for each complex matrix $A \in \mathbb{C}^{n \times n}$ with spectral abscissa $S(A)<0$ and for each vector norm $\vert\vert.\vert\vert$ in $\mathbb{C}^n$ to establish an explicit construction to obtain a matrix measure $\mu_{\vert\vert.\vert\vert}$ with $\mu_{\vert\vert.\vert\vert}(A)<0$. Furthermore the proved result is extended for the case when the entries $a_k^j$ of the matrix $A$ are continuous functions, i.e. $a_k^j \in C(K,\mathbb{C})$, where $K \subset \bar{\mathbb{C}_+}$ is an arbitrary compact set.

History

Received: July 14, 2017
Revised: June 10, 2017
Published: July 27, 2017

AMS Classification, Key Words

AMS Subject Classification: 15A60, 37C75, 65F35
Key Words and Phrases: matrix measure, logarithmic norm, Lozinskii measure, logarithmic efficiency, logarithmically optimal norm and matrix measure

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How to Cite?

DOI: 10.12732/ijpam.v115i3.16 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 3
Pages: 641 - 650


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