A sufficient condition for the super-linearization of polynomial systems

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We provide in this paper a sufficient condition for a polynomial dynamical system ẋ(t)=f(x(t)) to be super-linearizable, i.e., to be such that all its trajectories are linear projections of the trajectories of a linear dynamical system. The condition is expressed in terms of the hereby introduced weighted dependency graph G, whose nodes vi correspond to variables xi and edges vivj have weights [Formula presented]. We show that if the product of the edge weights along any cycle in G is a constant, then the system is super-linearizable. The proof is constructive, and we provide an algorithm to obtain super-linearizations and illustrate it on an example. Our result also provides a partial answer to an open question about polyflows.

Original languageEnglish (US)
Article number105588
JournalSystems and Control Letters
StatePublished - Sep 2023


  • Carleman linearization
  • Koopman linearization
  • Nonlinear systems
  • Super-linearization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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