Inverse Lyapunov Procedure

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 $J$ , of states $N$ and outputs $O$ . Optionally, a symmetric system can be enforced with the parameter $s = 1$ . The return value consists of three matrices; the system matrix $A$ , the input matrix $B$ and the output matrix $C$ .

[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 wikipedia:MATLAB MATLAB and wikipedia:GNU_Octave OCTAVE.

References

↑ S.C. Smith, J. Fisher, "On generating random systems: a gramian approach", Proceedings of the American Control Conference, 2003.

Contact

Christian Himpe

[smith03-1] S.C. Smith, J. Fisher, "On generating random systems: a gramian approach", Proceedings of the American Control Conference, 2003.

[1]