Abstract
We demonstrate that it is NP-hard to check whether all representatives of a square interval matrix share any of the following four properties: positive semidefiniteness, provided that the matrix is symmetric; norm ≤ 1; nonsingularity (NP-hardness of this particular problem was established recently by Poljak and Rohn); or stability (all eigenvalues in the open left half-plane).
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References
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This work was completed while on leave at INRIA-Rocquencourt, Domaine de Voluceau, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.
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Nemirovskii, A. Several NP-hard problems arising in robust stability analysis. Math. Control Signal Systems 6, 99–105 (1993). https://doi.org/10.1007/BF01211741
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DOI: https://doi.org/10.1007/BF01211741