HOME
Research Group Computational Methods in Systems and Control Theory

Diese Seite wird nicht mehr aktualisiert. Bitte besuchen Sie unsere neue Webpräsenz.

# MATLAB Codes for Computing the H∞-/L∞-Norm for Large-Scale Descriptor Systems

MATLAB implementation of various algorithms for the computation of the H-/L-norm for large-scale descriptor systems. Based on the computation of dominant poles two optimization methods were implemented to determine the norm value. Both implementations were tested with MATLAB 2012a under Linux and should work with a reasonably current version of MATLAB.

## Method 1: 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)

### Author

• Matthias Voigt, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.

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, please cite the publication stated below.

## Method 2: Computation of the L∞-Norm via Optimization on Level Sets

This algorithm is an extension of the well-known Bruinsma/Steinbuch 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

### Authors

• Ryan Lowe, Queens University, Ontario, Canada (main author);
• Matthias Voigt, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.