A note on block relative gain and Euclidean condition number

New relations between the block relative gain and condition number are developed that complement previously available results. It is shown 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 singular value. These results are useful in clarifying the role of block relative gain as a measure of potential design difficulties associated with a certain class of plants