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Linear Fractional Representation toolbox


The LFR toolbox was initially developed by Jean-François Magni (research director in ONERA) who passed away in January 2008. This toolbox is based on the notion of linear fractional representation, which extends the standard state-space representation to incorporate uncertainties and nonlinearities. The version 2.1 developed in 2006 and updated in 2014 can be downloaded on this page, as well as a complete documentation. Note that the LFR toolbox is not maintained anymore since 2014 and has been replaced with the GSS library in 2016.

License agreement, disclaimer

  • You are free to use any of the files of the LFR toolbox for personal or academic use. The express permission of the authors is required for any commercial use.
  • You can redistribute the LFR toolbox and its manual without modification provided that it is for a non commercial purpose. Redistribution in any commercial form (CD-ROM, USB flash drive or any other media) is hereby forbidden, unless with the express written permission of the authors. Any of your software developments related to this download will be available under similar license conditions.
  • Neither the authors nor ONERA accept any responsibility or liability with regard to this software that is licensed on an "as is" basis. There will be no duty on authors or ONERA to correct any errors or defects in the software.


Current version of the LFR Toolbox: v2.1 released on 1 April 2014 and revised by C. Roos and J-M. Biannic (ONERA)

Main changes:

  • implementation of a Simulink interface for LFR objects generation and simulation (see LFRLIB.slx and slk2lfr.m),
  • adaptation of symtreed.m and sym2lfr.m to ensure compatibility with MuPAD symbolic engine,
  • modification of distlfr.m to reduce computational time in case of a large number of uncertainties,
  • minor bugs fixed.

Older versions:

  • v2.0 released on 26 January 2006 and authored by J-F. Magni (ONERA), S. Hecker and A. Varga (DLR)
  • v1.3 released on 23 July 2004 and revised by J-F. Magni (ONERA)
  • v1.2 released on 14 April 2004 and revised by J-F. Magni (ONERA)
  • v1.1 released on 31 December 2003 and revised by J-F. Magni (ONERA)
  • v1.0 released on 28 February 2002 and authored by J-F. Magni (ONERA)

Download and install

  1. Download the LFR toolbox.
  2. Unzip the file in the folder of your choice (note that a complete documentation and several examples are included).
  3. Add this folder to the Matlab path.
  4. Enjoy, and do not hesitate to contact Jean-Marc Biannic ( or Clément Roos ( in case of trouble or success!


The LFR toolbox must be referenced when used in any published work:

[1] J-F. Magni, "Linear Fractional Representation toolbox for use with Matlab", February 2006, available with the SMAC Toolbox at