Asymptotically minimal contractors based on the centered form;Application to the stability analysis of linear systems

This paper proposes a new interval-based contractor for nonlinear equations which is minimal when dealing with narrow boxes. The method is based on the centered form classically used by interval algorithms combined with a Gauss Jordan band diagonalization preconditioning. As an illustration in stability analysis, we propose to compute the set of all parameters of a characteristic function of a linear dynamical system which have at least one zero in the imaginary axis. Our approach is able compute a guaranteed and accurate enclosure of the solution set faster than existing approaches.