Relations between block relative gain and Euclidean condition number

New relations between the block relative gain and condition number as well as the minimal condition number are developed. The results obtained show that the condition number must be large if the corresponding block relative gain has a large maximum singular value, and the minimal condition number must be large if the block relative gain has a large structured single value. These relations improve the previous result of C.N. Nett and V. Manousiouthakis (1987) and are useful in clarifying the role of block relative gain as a measure of potential design difficulties associated with plants that have large block relative gains