  In this paper, we propose a new method to measure the probabilistic
robustness of stochastic jump linear system with respect to both the initial
state uncertainties and the randomness in switching. Wasserstein distance which
defines a metric on the manifold of probability density functions is used as
tool for the performance and the stability measures. Starting with Gaussian
distribution to represent the initial state uncertainties, the probability
density function of the system state evolves into mixture of Gaussian, where
the number of Gaussian components grows exponentially. To cope with
computational complexity caused by mixture of Gaussian, we prove that there
exists an alternative probability density function that preserves exact
information in the Wasserstein level. The usefulness and the efficiency of the
proposed methods are demonstrated by example.
