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A system is Koopman super-linearizable if it admits a finite-dimensionalembedding as a linear system. Super-linearization is used to leverage methodsfrom linear systems theory to design controllers or observers for nonlinearsystems. We call a super-linearization balanced if the degrees of the hiddenobservables do not exceed the ones of the visible observables. We show thatsystems admitting such super-linearization can be put in a simple canonicalform via a linear change of variables.

Canonical forms for polynomial systems with balanced super-linearizations