mNo edit summary |
mNo edit summary |
||
| Line 6: | Line 6: | ||
==Description== | ==Description== | ||
The '''Inverse Lyapunov Procedure''' (ilp) is a synthetic random linear system generator. | The '''Inverse Lyapunov Procedure''' (ilp) is a synthetic random linear system generator. | ||
It is based on reversing the [[Balanced_Truncation]] procedure and was developed in <ref name="smith03">S.C. Smith, J. Fisher, "<span class="plainlinks">[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1243494 On generating random systems: a gramian approach]</span>", Proceedings of the American Control Conference, 2003.</ref>, where a description of the algorithm is given. | It is based on reversing the [[Balanced_Truncation|Balanced Truncation]] procedure and was developed in <ref name="smith03">S.C. Smith, J. Fisher, "<span class="plainlinks">[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1243494 On generating random systems: a gramian approach]</span>", Proceedings of the American Control Conference, 2003.</ref>, where a description of the algorithm is given. | ||
A central point is the solution of the Lyapunov equations for the system matrix instead of the gramian matrix. | A central point is the solution of the Lyapunov equations for the system matrix instead of the gramian matrix. | ||
| Line 23: | Line 23: | ||
The required [[Emgr|Empirical Gramian Framework]] can be obtained from [http://gramian.de/emgr.m http://gramian.de]. | The required [[Emgr|Empirical Gramian Framework]] can be obtained from [http://gramian.de/emgr.m http://gramian.de]. | ||
The '''ilp''' generator is compatible with [[wikipedia:MATLAB MATLAB]] and [[wikipedia:GNU_Octave OCTAVE]]. | The '''ilp''' generator is compatible with [[wikipedia:MATLAB|MATLAB]] and [[wikipedia:GNU_Octave|OCTAVE]]. | ||
==References== | ==References== | ||
Revision as of 14:57, 22 May 2013
Description
The Inverse Lyapunov Procedure (ilp) is a synthetic random linear system generator. It is based on reversing the Balanced Truncation procedure and was developed in [1], where a description of the algorithm is given.
A central point is the solution of the Lyapunov equations for the system matrix instead of the gramian matrix. This is feasable due to the symmetric (semi-)positive definiteness of the gramians and the requirement of a stable system. The solution will not be unique and include a symmetric system matrix, yet can be solved efficiently using empirical gramians.
Usage
To generate a random system using the Inverse Lyapunov Procedure download the M-file ilp.m. The function call requires three parameters; the number of inputs , of states and outputs . Optionally, a symmetric system can be enforced with the parameter . The return value consists of three matrices; the system matrix , the input matrix and the output matrix .
[A,B,C] = ilp(J,N,O,s);
The required Empirical Gramian Framework can be obtained from http://gramian.de. The ilp generator is compatible with MATLAB and OCTAVE.
References
- ↑ S.C. Smith, J. Fisher, "On generating random systems: a gramian approach", Proceedings of the American Control Conference, 2003.