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 and Control Letters, 15(1):1-7, July 1990. Conference paper appeared in Proceedings IEEE Conference on Decision and Control, pp.954-955, December 1989.

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 present a quadratically convergent algorithm for computing the mathbf{L}_infty-norm of a transfer matrix.