Sampled-Data Controller Synthesis for Minimizing the Worst-Timing-Type H2 Norm

• 成果类型: Article
• 署名作者: Kim, Jung Hoon; Hagiwara, Tomomichi
• 署名单位: Pohang University of Science & Technology (POSTECH); Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3672310
• 发表日期: 2026
• 关键词: TIME-SYSTEMS; SPACE APPROACH; H2; feedback; optimality

摘要

This note is concerned with the worst-timing-type (WT-type) H-2 norm of sampled-data systems. In continuous-time linear time-invariant systems, the total energy of the closed-loop impulse response is independent of the timing of the impulse. However, when the controller operates in a sampled-data fashion, this property no longer holds. The WT-type H-2 norm addresses this challenge by quantifying the supremal energy response that can arise from any impulse occurring between two consecutive sampling instants. In this context, a method for designing (full-order) discrete-time controller minimizing the WT-type H-2 norm of sampled-data systems is developed in this note. The approach consists of gridding treatment of the sampling intervals with N equally distant time instants and deriving N exact discretized models. We obtain a discrete-time controller exactly minimizing the maximum of the associated N discrete-time H-2 norms through the linear matrix inequality-based approach. We also show that the WT-type H-2 performance for the resulting approximately optimal controller via the gridding approach tends, in the order of 1/N, to the best achievable performance by the optimal controller. Finally, a numerical study is given to verify the overall arguments.