Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric

This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The realization of the state trajectory under stochastic jump processes becomes random variables, which brings forth the probability distributions for the system state. Therefore, a proper metric is necessary to measure the system performance with respect to stochastic switching. In this perspective, Wasserstein metric that assesses the distance between probability density functions is employed 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 the Wasserstein 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 that is commonly used for stochastic switching. The practical usefulness and efficiency of the proposed method are verified through numerical examples.