Existence and Completeness of Bounded Disturbance Observers: A Set-Membership Viewpoint

• 成果类型: Article
• 署名作者: Li, Yudong; Cong, Yirui; Dong, Jiuxiang
• 署名单位: Northeastern University - China; Northeastern University - China; National University of Defense Technology - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3496581
• 发表日期: 2025
• 页码: 2762-2769
• 关键词: Estimation error; uncertainty; discrete-time systems; Disturbance observers; SYMBOLS; observability; iterative methods; industries; Filtering theory; Benchmark testing; Boundedness; disturbance observer (DO)/estimation; set-membership filter; uncertain variables; worst-case optimality

摘要

This article investigates the boundedness of the disturbance observer (DO) for linear discrete-time systems. In contrast to previous studies that focus on analyzing and/or designing observer gains, our analysis and synthesis approach is based on a set-membership viewpoint. From this viewpoint, a necessary and sufficient existence condition of bounded DOs is first established, which can be easily verified. Furthermore, a set-membership filter-based DO is developed, and its completeness is proven; thus, our proposed DO is bounded if and only if bounded DOs exist. We also prove that the proposed DO has the capability to achieve the worst-case optimality, which can provide a benchmark for the design of DOs. Finally, numerical simulations are performed to corroborate the effectiveness of the theoretical results.