Linear Feedback Controller for Homogeneous Polynomial Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911580436824064 |
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| author | Cui, Shaoxuan Zhao, Qi Li, Guanlin Kojakhmetov, Hildeberto Jardon Cao, Ming |
| author_facet | Cui, Shaoxuan Zhao, Qi Li, Guanlin Kojakhmetov, Hildeberto Jardon Cao, Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08721 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear Feedback Controller for Homogeneous Polynomial Systems Cui, Shaoxuan Zhao, Qi Li, Guanlin Kojakhmetov, Hildeberto Jardon Cao, Ming Systems and Control 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. |
| title | Linear Feedback Controller for Homogeneous Polynomial Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.08721 |