Partial Exponential Stability Analysis of Slow-Fast Systems via Periodic Averaging

• 成果类型: Article
• 署名作者: Qin, Yuzhen; Kawano, Yu; Anderson, Brian D. O.; Cao, Ming
• 署名单位: University of California System; University of California Riverside; University of Groningen; Hiroshima University; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3117151
• 发表日期: 2022
• 页码: 5479-5486
• 关键词: Stability criteria; Synchronization; Laser stability; oscillators; Circuit stability; control theory; asymptotic stability; averaging; Kuramoto-Sakaguchi; partial exponen tial stability; remote synchronization

摘要

This article presents some new criteria for the partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by averaging over this fast scalar variable instead of the time variable. We show that the partial exponential stability of the averaged system implies that of the original one. We then apply the obtained criteria to the study of remote synchronization of Kuramoto-Sakaguchi oscillators coupled by a star network with two peripheral nodes. We show that detuning the natural frequency of the central mediating oscillator increases the robustness of the remote synchronization against phase shifts. This article appears to be the first-known attempt to analytically study the phase-unlocked remote synchronization.