A regularity result for the singular values of a transfer matrix and a
quadratically convergent algorithm for computing its L_infinity-norm
A regularity result for the singular values of a transfer matrix and a
quadratically convergent algorithm for computing its L_infinity-norm
S. Boyd and V. Balakrishnan
Systems & Control Letters, 15:1-7, 1990
Abstract: The ith singular value of a transfer matrix
need not be a differentiable function of
frequency where its multiplicity is greater than one.
We show that near a local maximum, however,
the largest singular value
has a Lipschitz second derivative,
but need not have a third derivative.
Using this regularity result,
we give a quadratically convergent
algorithm for computing the L_infinity-norm of a transfer matrix.
Keywords: Multi-input multi-output linear system,
transfer matrix, singular values, regularity of singular values,
L_infinity-norm, computation of L_infinity-norm, quadratic convergence,
H_infinity control.
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