A Unified Framework for Controller Synthesis via the Generalized KYP Lemma

• 成果类型: Article
• 署名作者: Huang, Guilin; Shakib, M. Fahim; Jaimoukha, Imad M.
• 署名单位: Imperial College London; Eindhoven University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3636431
• 发表日期: 2026
• 关键词: STATIC OUTPUT-FEEDBACK; POLE-PLACEMENT; linear-systems; DESIGN; inequalities; performance; STABILITY; h-2

摘要

Controller synthesis in control theory faces significant challenges due to the complexity of solving nonlinear matrix inequalities (NLMIs). Common methods, such as weighting filters and change-of-variable techniques, have drawbacks like increased system order and restrictive assumptions requiring a common Lyapunov variable. This article presents a unified framework that linearizes NLMIs without needing a common Lyapunov variable. Our approach handles continuous and discrete linear time-invariant systems, accommodating combinations of frequency intervals characterized by the Kalman-Yakubovich-Popov (KYP) and generalized KYP (gKYP) lemmas. It integrates a wide range of design specifications-including H-infinity, H-2, and passivity-applicable to any combination of input-output channels. Unlike traditional methods, our framework does not constrain the controller order and avoids weighting filters and gridding techniques. We introduce iterative algorithms that systematically improve performance over existing methods. By providing a unified solution to longstanding challenges in controller synthesis, our work offers an efficient tool for designing controllers for complex linear systems.