A Homotopy Theorem for Incremental Stability

• 成果类型: Article
• 署名作者: Chaffey, Thomas; Kharitenko, Andrey; Forni, Fulvio; Sepulchre, Rodolphe
• 署名单位: University of Sydney; University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich; KU Leuven
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3632433
• 发表日期: 2026
• 关键词: INPUT-OUTPUT STABILITY

摘要

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system, making no assumptions on the existence of an extended space, well-posedness, or causality. A first corollary of that result is that incremental stability may be verified by separation of scaled relative graphs, correcting two assumptions in (Chaffey et al., 2023, Thm. 2). Necessity of this correction is demonstrated by example. A second corollary provides an incremental version of the classical integral quadratic constraint stability theorem. Finally it is shown how to relax assumptions of incremental boundedness on the operators.