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Computation of the H∞-Norm via Optimization over Structured Pseudospectra

This algorithm is based on the relation between the H-norm and the structured complex stability radius of a transfer function. A nested iteration is used. In the inner iteration, the rightmost point of a structured ε-pseudospectrum is computed for a fixed ε. In the outer iteration, ε is updated via Newton steps to determine the value of ε for which the structured ε-pseudospectrum touches the imaginary axis.


Structured pseudospectra with most dominant poles (black crosses)


An inner iteration with intermediate iterates (black circles)


  • Matthias Voigt (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)


License and Usage

This software is published under the GNU General Public License, version 3. It is research code and there is no warranty for correctness of numerical results. This software uses the MATLAB implementation of the SAMDP algorithm (samdp.m) by Joost Rommes, which underlies own conditions. If you use this code for your own work, then please cite the publication stated below.

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