Existence and uniqueness of optimal matrix scalings
Existence and uniqueness of optimal matrix scalings
V. Balakrishnan and S. Boyd
SIAM J. on Matrix Analysis and Applications, 16(1):29--39, January 1995.
Abstract: 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. We
show 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, we derive a
sufficient condition for the uniqueness of the optimal
scaling.
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