Title :
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L ∞-norm
Author :
Boyd, S. ; Balakrishnan, V.
Author_Institution :
Stanford Univ., CA, USA
Abstract :
The ith singular value of a transfer matrix, σi(H(jω)), need not be a differential function of ω at frequencies where its multiplicity is greater than one. However, near a local maximum the largest singular value σ1(H(jω)) has a Lipschitz second derivative, but need not have a third derivative. On the basis of this regularity result, the authors obtain a quadratically convergent algorithm for computing the L∞-norm of a transfer matrix
Keywords :
convergence; matrix algebra; optimal control; transfer functions; L∞-norm; Lipschitz second derivative; local maximum; matrix algebra; optimal control; quadratically convergent algorithm; regularity; singular values; transfer matrix; Convergence; Frequency;
Conference_Titel :
Decision and Control, 1989., Proceedings of the 28th IEEE Conference on
Conference_Location :
Tampa, FL
DOI :
10.1109/CDC.1989.70267