In a nutshell, TMsim is a tool for the analysis of a dynamical system with uncertainties, arising e.g. from the manufacturing process, external parameters like temperature, or possible unknown device characteristics. The tool is implemented in Matlab, open source and freely available to all researchers, thus becoming a common platform for practicing and for stimulating further improvements, extensions and applications (download here).


The theory underlying TMsim is best described in:

[1] R. Trinchero, P. Manfredi, T. Ding, I. S. Stievano, "Combined Parametric and Worst Case Circuit Analysis via Taylor Models", IEEE Trans. Circuits and Systems - I: regular papers, Vol. 63, No. 7, pp. 1067-1078, Jul. 2016 (ieeexplore link, authors' copy ).

[2] R. Trinchero, P. Manfredi, and I.S. Stievano, "TMsim: an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties", Mathematical Problems in Engineering, Volume 2017 (2017), Article ID 6739857, 12 pages (link).

TMsim was made available in Oct. 2016 as public domain Matlab-based routines. The tool is provided along with some simple tutorial examples aimed at illustrating the method. More attractive and real-world applications are presented in [1,2].

Copyright (C) 2016 - Riccardo Trinchero, Paolo Manfredi, Igor Simone Stievano

Restrictions of use: embedding the program code in any commercial software is strictly prohibited. If the code is used in a scientific work, then reference should be made to the above publications [1,2].

Contact info:,, (R. Trinchero and I.S. Stievano are with the EMC Group, Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy and P. Manfredi is with the Electromagnetics Group, Department of Information Technology, Ghent University, Gent, Belgium)


Theoretical framework: A combined parametric and worst-case algorithmic technique based on the robust theoretical framework of the so-called Taylor Models (TM) is used. The system response is represented by means of the sum of a multivariate polynomial with an interval remainder accounting for the approximation error. While the polynomial part provides an accurate, analytical and parametric representation of the response as a function of the selected design parameters, the complementary information on the remainder error yields a conservative, yet tight, estimation of the worst case bounds. Both state-of-the-art solutions and ad-hoc improvements are used to handle the basic scalar operations (such as sums, subtractions, multiplications, complex-valued algebra and nonlinear operators) and suitably extended to matrix operation (e.g., including the delicate aspect of matrix inversion). The TM representation of the output response of a system (either defined in terms of a frequency-domain transfer function or as a time-domain response) is obtained by propagating the input uncertainties to the output response via a suitable redefinition of all the basic operations involved in the system analysis.