Mean Square Stability for Stochastic Jump Linear Systems via Optimal Transport

TL;DR

This paper introduces a unified framework using optimal transport and Wasserstein metrics to analyze mean square stability in stochastic jump linear systems, applicable beyond Markovian assumptions.

Contribution

It presents a novel stability analysis method based on Wasserstein distance that applies to general stochastic jump linear systems without Markovian assumptions.

Findings

The framework guarantees mean square stability using Wasserstein distance.

It recovers existing stability conditions as special cases.

Applicable to non-Markovian jump processes.

Abstract

In this note, we provide a unified framework for the mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric known as an optimal transport, that assesses the distance between probability density functions enables the stability analysis. Without any assumption on the underlying jump process, this Wasserstein distance guarantees the mean square stability for general stochastic jump linear systems, not necessarily for Markovian jump. The validity of the proposed methods are proved by recovering already-known stability conditions under this framework.