2025/11/13 by Wouter Jongeneel, Jongeneel, Wouter
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2511.10429
openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
The notion of an attractor has various definitions in the theory of dynamical systems. Under compactness assumptions, several of those definitions coincide and the theory is rather complete. However, without compactness, the picture becomes blurry. To improve our understanding, we characterize in this work when a closed, not necessarily compact, asymptotically stable attractor on a locally compact metric space is homotopy equivalent to its domain of attraction. This enables a further structural study of the corresponding feedback stabilization problem.