Flatness for linear fractional systems with application to a thermal system

This paper is devoted to the study of the flatness property of linear time-invariant differential systems of fractional systems. We give two characterizations of fractionally flat outputs and algorithms to compute them. We then present an application to a two dimensional thermal system that we approximate by a fractional model of order 1 2 , that is fractionally flat. Trajectory planning of the temperature at a given point is then deduced without integration of the system equations and simulations are presented. Index Terms Polynomial matrices, fractional derivative, fractional systems, differential flatness, fractional flatness, fractional flat output, thermal system, trajectory planning.