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Computation of the L∞-Norm via Optimization on Level Sets

This algorithm is an extension of the well-known Boyd/Balakrishnan algorithm to large-scale problems. Using the dominant poles of the transfer function, shifts for a structure-preserving iterative eigensolver for even eigenvalue problems (even IRA) are computed. The obtained imaginary eigenvalues can now be used to determine level sets that contain the optimal frequency.


Plot of a transfer function with computed norm value (red circle)


Plot of the level sets for every iteration


  • Ryan Lowe (McGill University, Québec, Canada (main author))
  • 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 implementations of the SAMDP algorithm (samdp.m) by Joost Rommes and the even IRA (even_ira.m) by Volker Mehrmann, Valeria Simoncini, and Christian Schröder, which underly own conditions. If you use this code for your own work, then please cite the publications stated below.


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Auxiliary Functions