Abstract
This paper is concerned with the diagonal dominance. The diagonal dominance is the property that the diagonal elements are relatively larger than the off-diagonal elements. And it is an important property for multivariable feedback systems with diagonal controllers.
The original diagonal dominance was defined by 1-norm or ∞-norm, where the matrix p-norms are induced norms. And generalizations were made by using either scaling or Perron-Frobenius root. But all the dominance loose the phase information, because these depend only on the absolute values of each elements of the matrix.
This paper proposes a new diagonal dominance defined by 2-norm. This diagonal dominance is less conservative than the other dominance. This paper also clarifies the relation between the diagonal dominance and strictly positive realness.
