1. Partial Exponential Stability Analysis of Slow-Fast Systems via Periodic Averaging
- Author
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Yu Kawano, Ming Cao, Yuzhen Qin, Brian D. O. Anderson, and Discrete Technology and Production Automation
- Subjects
0209 industrial biotechnology ,Work (thermodynamics) ,Stability criteria ,Asymptotic stability ,Phase (waves) ,Laser stability ,Partial exponential stability ,02 engineering and technology ,Systems and Control (eess.SY) ,Synchronization ,Electrical Engineering and Systems Science - Systems and Control ,Circuit stability ,020901 industrial engineering & automation ,0203 mechanical engineering ,Exponential stability ,Robustness (computer science) ,Control theory ,FOS: Electrical engineering, electronic engineering, information engineering ,Oscillators ,Statistical physics ,Electrical and Electronic Engineering ,Mathematics ,averaging ,020301 aerospace & aeronautics ,Kuramoto-Sakaguchi ,Natural frequency ,Computer Science Applications ,Nonlinear system ,Control and Systems Engineering ,remote synchronization - Abstract
This paper presents some new criteria for 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 then show that partial exponential stability of the averaged system implies partial exponential stability of the original one. As some intermediate results, we also obtain a new converse Lyapunov theorem and some perturbation theorems for partially exponentially stable systems. We then apply our established criteria to study remote synchronization of Kuramoto-Sakaguchi oscillators coupled by a star network with two peripheral nodes. We analytically show that detuning the natural frequency of the central mediating oscillator can increase the robustness of the remote synchronization against phase shifts.
- Published
- 2022
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