Abstract
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 language | English (US) |
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Article number | 105588 |
Journal | Systems and Control Letters |
Volume | 179 |
DOIs | |
State | Published - Sep 2023 |
Keywords
- 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