Linear Feedback Controller for Homogeneous Polynomial Systems
For control theorists working on polynomial systems, this offers a computationally efficient alternative to local linearization or SOS methods, though limited to systems with ODECO structure.
This paper proposes a structure-preserving linear feedback controller for homogeneous polynomial systems with orthogonally decomposable tensor dynamics, enabling closed-form trajectory expressions and sharp region-of-attraction estimates. The approach avoids conservative Lyapunov/SOS methods and provides explicit convergence thresholds.
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.