Linear Feedback Controller for Homogeneous Polynomial Systems
Abstract
This paper studies stabilization and its corresponding closed-loop region-of-attraction (ROA) for homogeneous polynomial dynamical systems whose nonlinear term admits an orthogonally decomposable (ODECO) tensor representation. While recent tensor-based results provide explicit solutions and sharp global characterizations for open-loop ODECO systems, closed-loop synthesis and computable ROA estimates are still often dominated by local linearization or Lyapunov/SOS (sum of squares) methods, which can be conservative and computationally demanding. We propose a structure-preserving linear feedback design that shares the ODECO eigenbasis of the system's tensor, thereby enabling closed-form trajectory expressions, explicit convergence/escape thresholds, and sharp ROA characterizations. Under mild conditions, we further derive robustness/ISS-type bounds for bounded disturbances. Numerical examples validate the theoretical results.
Cite
@article{arxiv.2604.08721,
title = {Linear Feedback Controller for Homogeneous Polynomial Systems},
author = {Shaoxuan Cui and Qi Zhao and Guanlin Li and Hildeberto Jardon Kojakhmetov and Ming Cao},
journal= {arXiv preprint arXiv:2604.08721},
year = {2026}
}