Canonical forms for polynomial systems with balanced super-linearizations

2022/12/22 by M. -A. Belabbas, Belabbas, M. -A.
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2212.12054

openalex publication_date 2022/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to design controllers or observers for nonlinear systems. We call a super-linearization balanced if the degrees of the hidden observables do not exceed the ones of the visible observables. We show that systems admitting such super-linearization can be put in a simple canonical form via a linear change of variables.

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