Contraction Analysis of Discrete-Time Stochastic Systems

• 成果类型: Article
• 署名作者: Kawano, Yu; Hosoe, Yohei
• 署名单位: Hiroshima University; Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3283678
• 发表日期: 2024
• 页码: 982-997
• 关键词: Contraction; discrete-time systems; incremental stability; Nonlinear systems; Stochastic systems

摘要

In this article, we develop a novel contraction framework for the 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., independent and identically distributed processes and Markov processes, which are demonstrated as selected applications of our results.