Robust simulation of rational discrete-time systems via sum of squares relaxations

Abstract

Abstract This paper concerns the simulation of a class of nonlinear discrete-time systems under a set of initial conditions described by an ellipsoid. We derive a procedure allowing the propagation of such ellipsoids through time, which makes it possible to set a guaranteed hard bound on the evolution of the state of the system for all the possible initial conditions. At the end of the paper, we show an application of the method through three academics examples, two of which are taken from the theory of fractals.