Generalized Necessary and Sufficient Robust Boundedness Results for Feedback Systems

• 成果类型: Article
• 署名作者: Cyrus, Saman; Lessard, Laurent
• 署名单位: Northeastern University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3222755
• 发表日期: 2023
• 页码: 5693-5698
• 关键词: Conic sectors; input-output stability; Necessary and sufficient conditions; Nonlinear systems; Robust control; stability analysis

摘要

Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. In this article, we present a generalized version of these results for arbitrary semi-inner product spaces. Our result is purely algebraic, and holds even when the conventional discrete or continuous-time causal dynamical systems are replaced by general nonlinear relations, where there need not exist a notion of time. Our result clarifies when the sufficient conditions for robust stability are also necessary, and explains why stronger assumptions, such as linearity and time-invariance are typically needed to prove necessity in the conventional dynamical systems setting.