Canonical forms for polynomial systems with balanced super-linearizations

TL;DR

This paper introduces a canonical form for polynomial systems that admit balanced super-linearizations, simplifying their analysis and control design by leveraging linear system theory.

Contribution

It establishes that systems with balanced super-linearizations can be transformed into a canonical form through linear change of variables.

Findings

Balanced super-linearizable systems can be expressed in a simplified canonical form.

The canonical form facilitates the application of linear control methods to nonlinear systems.

The approach provides a systematic way to analyze polynomial systems with super-linearizations.

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.