Contraction Analysis of Discrete-time Stochastic Systems
Systems and Control
2021-06-11 v1 Systems and Control
Optimization and Control
Abstract
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for uniform incremental exponential stability (UIES) in the first moment with respect to a Riemannian metric. Then, focusing on the Euclidean distance, we present a necessary and sufficient condition for UIES in the second moment. By virtue of studying general stochastic processes, we can readily derive UIES conditions for special classes of processes, e.g., i.i.d. processes and Markov processes, which is demonstrated as selected applications of our results.
Keywords
Cite
@article{arxiv.2106.05635,
title = {Contraction Analysis of Discrete-time Stochastic Systems},
author = {Yu Kawano and Yohei Hosoe},
journal= {arXiv preprint arXiv:2106.05635},
year = {2021}
}