Converse Theorems for Integral Quadratic Constraints

• 成果类型: Article
• 署名作者: Khong, Sei Zhen; Kao, Chung-Yao
• 署名单位: University of Hong Kong; National Sun Yat Sen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3024269
• 发表日期: 2021
• 页码: 3695-3701
• 关键词: Linear systems; Robustness; uncertainty; Stability criteria; Computed tomography; STANDARDS; integral quadratic constraints (IQCs); Passivity; robust stability; small gain

摘要

A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is stable, then the given system must necessarily satisfy the complementary IQC. These theorems are specialized to derive multiple versions of converse passivity results. They cover standard notions of strict passivity as well as passivity indices that characterize the tradeoffs between passivity surplus and deficit. Converse frequency-weighted small-gain and passivity theorems are also established.