Publication Date:
2016-07-13
Description:
We present a new scaleable algorithm for approximating the $H_{\infty }$ norm, an important robust stability measure for linear dynamical systems with input and output. Our spectral-value-set-based method uses a novel hybrid expansion–contraction scheme that, under reasonable assumptions, is guaranteed to converge to a stationary point of the optimization problem defining the $H_{\infty }$ norm, and, in practice, typically returns local or global maximizers. We prove that the hybrid expansion–contraction method has a quadratic rate of convergence that is also confirmed in practice. In comprehensive numerical experiments, we show that our new method is not only robust but exceptionally fast, successfully completing a large-scale test set 25 times faster than an earlier method by Guglielmi, Gürbüzbalaban & Overton (2013, SIAM J. Matrix Anal. Appl. , 34 , 709–737), which occasionally breaks down far from a stationary point of the underlying optimization problem.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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