This project contains the REDUCE source files for several decision problems occurring in static output feedback design of linear time-invaraint systems. The decision problems are formally solved using quantifier elimination.
Röbenack, K., Voßwinkel, R.:
Eigenvalue placement by quantifier elimination-the static output feedback problem.
Acta Cybernetica, 24(3), 409-427, 2020.
You need to install the computer algebra system REDUCE. The REDUCE distribution is available for several operating systems:
http://reduce-algebra.sourceforge.net/
There are two main versions of REDUCE available, which are based on different Lips libraries:
| Command | Library version |
|---|---|
redcsl |
Codemist Standard Lisp (CSL) |
redpsl |
Portable Standard Lisp (PSL) |
The quantifier elimination is carried out using the package REDLOG. The program code is already part of REDUCE. The documentation can be found on the REDLOG website:
To illustrate our approach we modified Example 4.1 from the following reference:
Yannakoudakis, A. G.:
The static output feedback from the invariant point of view.
IMA Journal of Mathematical Control and Information 33(3):639-668, 2016.
The example systems consists of the following matrices:
We consider different structures of the 2×2 gain matrix:
The src directory contains the source REDUCE files listed in the next table. These files differ in the geometry of the bounds and the problem formulation.
| File | Description |
|---|---|
ex-place-arbitrary.red |
Test of arbitrary eigenvalue assignability |
ex-place-special.red |
Test of a special eigenvalue assignability |
ex-stab.red |
Test of stabilizability |
ex-stab-real.red |
Test of real stabilizability |
This project is licensed under the GNU General Public License v3.0 - see the LICENSE file for details.