T. Mori and H. Kokame, "Comments of `On the stability of discrete-time linear interval systems' ", Automatica, 1995, Vol. 31, No. 6, pp. 921-922.

The authors comment on the paper by P. Myszkorowski published in Automatica, 1994, Vol. 30, pp. 913-914. In that paper, the author proposes a new sufficient condition for stability of discrete-time linear systems \$x_{k+1}=A(k)x_k\$, where for every \$k\$, components \$a_{ij}(k)\$ of the matrix \$A(k)\$ belong to the known intervals \$[a^-_{ij},a^+_{ij}]\$. Myszkorowski's criterion is difficult to check. The authors show that his criterion is equivalent to the easily checkable fact that \$I-B\$ is an \$M-\$matrix, where \$I\$ is a unit matrix, \$b_{ij}=\max(|a^-_{jj}|,|a^+_{ij}|)\$, and an \$M-\$matrix is a matrix with non-positive off-diagonal entries for which successive leading principal minors are all positive.