Contraction Analysis of Differentially Positive 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.2025.3543562
• 发表日期: 2025
• 关键词: SEPARABLE LYAPUNOV FUNCTIONS; monotone systems; STABILITY; METRICS; DESIGN

摘要

In this article, we examine the role of differential positivity in the contraction analysis of discrete-time nonlinear systems with parameters that follow stochastic processes. We investigate the concept of almost sure differential positivity, which parallels the positivity of linear systems, and utilize it to derive vector-type sufficient conditions for uniform incremental exponential stability in the first moment. Employing these conditions, we demonstrate that network stability analysis can be made scalable by decomposing it into analysis of subcomponents and interconnection structures. Our results are applicable to a range of systems, including nonlinear Markov jump systems, nonlinear deterministic systems, and linear stochastic systems, by specifying the system structures. In addition, we perform converse analysis for almost surely cooperative systems, i.e., almost surely differentially positive systems with respect to the positive orthant cones.