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

Abstract

This paper focuses on the performance and robustness analysis of stochastic jump linear systems. In the presence of stochastic jumps, state variables evolve as random process, with associated time varying probability density functions. Consequently, system analysis is performed at the density level and a proper metric is necessary to quantify the system performance. In this paper, Wasserstein metric that measures a distance between probability density functions is employed to develop new results for the performance analysis of stochastic jump linear systems. Both transient and steady-state performance of the systems, with given initial state uncertainties, can be analyzed in this framework. Also, we prove that the convergence of the Wasserstein metric implies the mean square stability. We present a novel “Split-and-Merge” algorithm for propagation of state uncertainty in such systems. Overall, this study provides a unifying framework for the performance and robustness analysis of general stochastic jump linear systems, and not necessarily Markovian that is commonly assumed. The usefulness and efficiency of the proposed method are verified through numerical examples.