Matlab programs for reduced-order controller design

We provide Matlab programs to check the numerical examples of model reduction (MR) shown in Sections 4.1 and 4.2 of

• M. Nagahara, Y. Iwai, and N. Sebe, Projection onto the Set of Rank-constrained Structured Matrices for Reduced-order Controller Design, submitted to Algorithms, 2022.

Matlab programs

You need to place the following m-files in the same folder of the main programs.

• reduced_order_controller_stability.m (main program for Sections 4.1 and 4.2)
• reduced_order_controller_hinf_bisection.m (main program for Section 4.3)
• Proj_LMI.m (projection operator for the LMIs)
• Proj_rank.m (projection operator for the rank condition)
• controller_realization.m (controller realization from X and Y)
• retrieve_eliminated.m (used in controller_realization.m)
• s_sparse_operator.m (s-sparse operator for truncation)

Requirements

To run hinfstruct for nonsmooth H-infinity synthesis, you need Robust Control Toolbox. You also need to install Yalmip, SDPT3, SeDuMi, and COMPLeib to run the main program.

• Yalmip can be downloaded from https://yalmip.github.io/
• SDPT3 can be downloaded from https://github.com/SQLP/SDPT3
• SeDuMi can be downloaded from https://sedumi.ie.lehigh.edu/
• COMPLeib can be downloaded from http://www.complib.de/

Results of stability tests for 95 bemchmark models

The results of stability tests for 95 benchmark models are shown in the following exel file:

• stability_data.xlsx