  This paper focuses on the performance and the robustness analysis of
stochastic jump linear systems. The state trajectory under stochastic jump
process becomes random variables, which brings forth the probability
distributions in the system state. Therefore, we need to adopt a proper metric
to measure the system performance with respect to stochastic switching. In this
perspective, Wasserstein metric that assesses the distance between probability
density functions is applied to provide the performance and the robustness
analysis. Both the transient and steady-state performance of the systems with
given initial state uncertainties can be measured in this framework. Also, we
prove that the convergence of this metric implies the mean square stability.
Overall, this study provides a unifying framework for the performance and the
robustness analysis of general stochastic jump linear systems, but not
necessarily Markovian jump process that is commonly used for stochastic
switching. The practical usefulness and efficiency of the proposed method are
verified through numerical examples.
