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Title: Contraction Analysis of Discrete-Time Stochastic Systems
Authors: Kawano, Yu
Hosoe, Yohei
Author's alias: 河野, 佑
細江, 陽平
Keywords: Nonlinear systems
stochastic systems
discrete-time systems
contraction
incremental stability
Issue Date: Feb-2024
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Journal title: IEEE Transactions on Automatic Control
Volume: 69
Issue: 2
Start page: 982
End page: 997
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., independent and identically distributed (i.i.d.) processes and Markov processes, which is demonstrated as selected applications of our results.
Description: 非線形確率モデルの安定性理論 --機械学習と自動化技術の橋渡し--. 京都大学プレスリリース. 2023-07-05.
Rights: © 2023 The Authors.
This work is licensed under a Creative Commons Attribution 4.0 License.
URI: http://hdl.handle.net/2433/286845
DOI(Published Version): 10.1109/TAC.2023.3283678
Related Link: https://www.t.kyoto-u.ac.jp/ja/research/topics/20230704
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