Some first thoughts on the stability of the asynchronous systems

TL;DR

This paper explores the stability of asynchronous systems modeled as multi-valued functions, focusing on non-initialized, non-deterministic systems inspired by asynchronous circuit modeling.

Contribution

It introduces the problem of stability analysis for non-initialized, non-deterministic asynchronous systems, a topic not extensively addressed before.

Findings

Defines the stability problem for asynchronous systems

Highlights the challenges in analyzing non-deterministic models

Provides a foundation for future stability criteria development

Abstract

The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous circuits. Our purpose is to state the problem of the their stability.