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

TL;DR

This paper introduces a new minimal interval contractor based on centered form and preconditioning, enabling faster and guaranteed enclosure of solutions for stability analysis of linear systems.

Contribution

It presents a novel minimal contractor method combining centered form with Gauss Jordan preconditioning for nonlinear equations.

Findings

Faster computation of solution sets compared to existing methods

Guaranteed enclosures of solutions for stability analysis

Effective handling of narrow boxes in interval computations

Abstract

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.