The block bialternate sum for partitioned matrices is introduced in th
is paper and its basic properties are established. Using the block bia
lternate sum, exact values of the maximal stability range of the param
eter in integral control systems and singularly perturbed systems as a
lso the minimal range of the gain parameter in a high-gain feedback sy
stem are determined. The proposed method is claimed to be computationa
lly superior to all other existing methods.