L2-Gain Analysis of Periodic Event-Triggered Control and Self-Triggered Control Using Lifting

• 成果类型: Article
• 署名作者: Strijbosch, Nard; Dullerud, Geir E.; Teel, Andrew R.; Heemels, W. P. M. H.
• 署名单位: Eindhoven University of Technology; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3025304
• 发表日期: 2021
• 页码: 3749-3756
• 关键词: Networked control systems; periodic event-triggered control (PETC); piecewise affine (PWA) systems; self-triggered control (STC)

摘要

We analyze the stability, and L-2-gain properties of a class of hybrid systems that exhibit time-varying linear flow dynamics, periodic time-triggered jumps, and arbitrary nonlinear jump maps. This class of hybrid systems encompasses periodic event-triggered control, self-triggered control, and networked control systems including time-varying communication delays. New notions on the stability, and contractivity (L-2-gain strictly smaller than 1) from the beginning of the flow, and from the end of the flow are introduced, and formal relationships are derived between these notions, revealing that some are stronger than others. Inspired by ideas from lifting, it is shown that the internal stability, and contractivity in L-2-sense of a continuous-time hybrid system in the framework is equivalent to the stability, and contractivity in l(2)-sense (meaning the l(2)-gain is smaller than 1) of an appropriate time-varying discrete-time nonlinear system. These results recover existing works in the literature as special cases, and indicate that analysing different discrete-time nonlinear systems (of the same level of complexity) than in existing works yield stronger conclusions on the L-2-gain.