# Global stability of almost periodic solutions of monotone sweeping processes and their response to non-monotone perturbations

## TL;DR

This paper establishes the global stability of almost periodic solutions in monotone sweeping processes and analyzes their robustness under non-monotone perturbations, providing a comprehensive qualitative theory for these dynamical systems.

## Contribution

It introduces a new theoretical framework for the stability and perturbation response of almost periodic solutions in sweeping processes, extending previous results to non-monotone cases.

## Key findings

- Existence of globally exponentially stable almost periodic solutions in monotone sweeping processes.
- Persistence of stability under certain non-monotone perturbations.
- Qualitative understanding of the dynamics of both monotone and non-monotone sweeping processes.

## Abstract

We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone right-hand-sides admits a globally exponentially stable almost periodic solution. And then we describe the extent to which such a globally stable solution persists under non-monotone perturbations.