Existence and Uniqueness of Optimal Matrix Scalings
V. Balakrishnan, Suzanne Hruska Boyd · SIAM Journal on Matrix Analysis and Applications · 1995
The problem of finding a diagonal similarity scaling to minimize the scaled singular value of a matrix arises frequently in robustness analysis of control systems. It is shown here that the set of optimal diagonal scalings is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an irreducible matrix, a sufficient condition is derived for the uniqueness of the optimal scaling.