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A new framework for Mean Square Stability of Stochastic Jump Linear Systems via Optimal Transport

In this paper, we provide a new framework for mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric which defines an optimal transport cost between probability density functions enables the stability analysis. Without any assumptions on the nature of the underlying jump process, the convergence of the Wasserstein distance guarantees the mean square stability for general stochastic jump linear systems, not just Markovian processes. The validity of the proposed methods are proved by recovering already-known stability conditions under this framework.