# Stabilizing switching signals: a transition from point-wise to asymptotic conditions

## TL;DR

This paper introduces a unified framework for stabilizing switching signals in switched systems, bridging point-wise and asymptotic conditions, and encompassing prior results within a comprehensive approach.

## Contribution

It proposes a new general class of stabilizing switching signals and unifies existing point-wise and asymptotic stability conditions under one framework.

## Key findings

- New class of stabilizing switching signals introduced
- Unified approach encompasses prior point-wise and asymptotic results
- First comprehensive framework linking different stability conditions

## Abstract

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an umbrella framework. We achieve this in two steps: Firstly, given a family of systems, possibly containing unstable dynamics, we propose a new and general class of stabilizing switching signals. Secondly, we demonstrate that prior results based on both point-wise and asymptotic characterizations follow our result. This is the first attempt in the switched systems literature where these switching signals are unified under one banner.