Improving Rohn approximation for the real parts of interval matrix eigenvalues

The paper proposes a new approximation method for the upper and lower bounds of the real parts of interval matrix eigenvalues. As a theoretical support, we exploit the properties of the matrix measures corresponding to monotonic (or, equivalently, absolute) vector norms. The numerical approach focuses on the use of the results derived for the matrix measure defined by the Euclidean norm (or 2-norm). The computational procedure is formulated as a minimization problem of a linear objective function constrained by bilinear matrix inequalities. We prove (by mathematical arguments and, separately, by examples) that our estimations are better or, at least, as accurate as those provided by the method due to Rohn (see reference [6]).