MATLAB ROUTINES
For questions, comments e-mail to: emengi@ku.edu.tr
These routines maximize the distance to instability from an affine matrix-valued function A(x) over the parameters x subject to box constraints. A particular problem that falls into this scope is robust stabilization by output feedback, i.e., for a given square matrix A, tall and skinny B, short and fat C, maximization of the distance instability from A+BKC over the variable K whose entries are constrained to lie in prescribed intervals.
The algorithms are to locate a global maximizer, and discussed in [Mengi 2018] below. They are meant when there are only a few parameters; at this point I have not tested them on problems with more than two parameters.
Download the Routines
Large-scale problems
Based on a greedy subspace framework [Mengi 2018, Sections 3-5]
Small-scale problems
Based on upper support functions [Mengi 2018, Section 2]
Usage
The main routines to call are subspace_max_distinstab_du.m for large-scale problems, and max_distinstab_main.mfor small-scale problems.
For their usage see the sample calls. If it is still not clear how to call them, please see the comments at the beginning of these main routines.
Below are the test examples that are used in the paper [Mengi 2018].
Section 2.4
- 4×4 random example in Section 2.4
- Turbo-generator example in Section 2.4
- 200×200 random example in Section 2.4
Section 7.1
Section 7.2
- 400×400 example in Section 7.2
- 800×800 example in Section 7.2
- 1200×1200 example in Section 7.2
- 1600×1600 example in Section 7.2
- 2000×2000 example in Section 7.2
Reference
[Mengi 2018] E. Mengi. Large-Scale and Global Maximization of the Distance to Instability.