A characterization of strong regularity of interval matrices

Abstract

As the main result of this paper it is proved that an interval matrix [Ac −∆,Ac +∆] is strongly regular if and only if the matrix inequality M(I − |I − RAc| − |R|∆) ≥ I has a solution, where M and R are real square matrices and M is nonnegative. Several consequences of this result are drawn.