Ústav přístrojové a řídicí techniky

Quasi-Polynomial Mapping Based Rootfinder

QPmR v.2 is a Matlab function for computation and analysis of spectrum of characteristic quasi-polynomials of both retarded and neutral time delay systems. It utilizes algorithms described in:

# Vyhlídal, T. – Zítek, P.: Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros. IEEE Transactions on Automatic Control. 2009, vol. 54, no. 1, p. 171-177. ISSN 0018-9286.

# Vyhlídal, T. and Zítek, P., (2003), Quasipolynomial mapping based rootfinder for analysis of time delay systems, Time Delay Systems 2003 – A Proceedings volume from the 4th IFAC workshopRocquencourt, France, Elsevier: Oxford, pp. 227-232.

# Michiels, W. – Vyhlídal, T.: An Eigenvalue Based Approach for the Stabilization of Linear Time-Delay Systems of Neutral Type. Automatica. 2005, vol. 41, no. 6, p. 991-998. ISSN 0005-1098.

QPmR download

Manual download

Detailed algorithm description together with examples can be found in

# Vyhlídal, T. – Zítek, P.: QPmR v.2 – Quasipolynomial rootfinder, algorithm and examples. to appear in Advances in Delays and Dynamics, Editors: Vyhídal T., Lafay J.F., Sipahi R., Sringer 2013.

The former algorithm implementations can be found here (These Matlab functions require Symbolic Math Toolbox. The version 2 of QPmR algorithm was completely reprogrammed).


Licence conditions: The Matlab function QPmR is a freely available software tool for non-commercial use. It is provided as it is, without any express or implied warranty. In no event, the authors are liable for any error in the software tool, any misuse of it or any damage arising out of its use. The entire risk of using the software lies with the party doing so. Any use of the software tool constitutes acceptance of the terms of the above statement.


Please, do not hesitate to mail to Tomáš Vyhlídal for questions and comments.