Mean Square Stability for Stochastic Jump Linear Systems via Optimal Transport

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.