  In this study, the problem of robust Schur stability of $n\times n$
dimensional matrix segments by using the bialternate product of matrices is
considered. It is shown that the problem can be reduced to the existence of
negative eigenvalues of two of three specially constructed matrices and the
existence of eigenvalues belonging to the interval $[1,\infty)$ of the third
matrix. A necessary and sufficient condition is given for the convex
combinations of two stable matrices with rank one difference to be robust Schur
stable. It is shown that the robust stability of the convex hull of a finite
number of matrices whose two-by-two differences are of rank $1$ is equivalent
to the robust stability of the segments formed by these matrices. Examples of
applying the obtained results are given.
