Probabilistic Robustness Analysis of Stochastic Jump Linear Systems

Abstract: 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.