Duality Bounds for Discrete-Time Zames-Falb Multipliers

• 成果类型: Article
• 署名作者: Zhang, Jingfan; Carrasco, Joaquin; Heath, William Paul
• 署名单位: University of Manchester
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3095418
• 发表日期: 2022
• 页码: 3521-3528
• 关键词: Machine-to-machine communications; Stability criteria; Power system stability; Numerical stability; Prediction algorithms; optimization; Linear systems; Absolute stability; duality bounds; Zames-Falb multipliers

摘要

This note presents phase conditions under which there is no suitable Zames- Falb multiplier for a given discrete-time system. Our conditions can be seen as the discrete-time counterpart of Jonsson's duality conditions for Zames-Falb multipliers. By contrast with their continuous-time counterparts and other phase limitations in the literature, they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. The numerical results allow us to conclude that the current state-of-the-art in searches for Zames-Falb multipliers is not conservative. Moreover, they allow us to show, by construction, that the set of plants for which a suitable Zames- Falb multiplier exists is nonconvex.