Interval centred form for proving stability of non-linear discrete-time systems

TL;DR

This paper introduces a novel interval centred form approach using stability contractors to efficiently prove the asymptotic stability of non-linear discrete-time systems, demonstrated through theoretical and practical examples.

Contribution

The paper presents a new method leveraging interval centred form and stability contractors for stability analysis of non-linear discrete systems, enhancing proof simplicity and practical applicability.

Findings

Effective proof of asymptotic stability using the new approach

Application to robot trajectory stability and localization systems

Theoretical validation through illustrative examples

Abstract

In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and makes it possible to easily prove asymptotic stability of a discrete system. Then, we illustrate the principle of our approach through theoretical examples. Finally, we provide two practical examples using our method : proving stability of a localisation system and that of the trajectory of a robot.