  Quadratization refers to a transformation of an arbitrary system of
polynomial ordinary differential equations to a system with at most quadratic
right-hand side. Such a transformation unveils new variables and model
structures that facilitate model analysis, simulation, and control and offers a
convenient parameterization for data-driven approaches. Quadratization
techniques have found applications in diverse fields, including systems theory,
fluid mechanics, chemical reaction modeling, and mathematical analysis.
  In this study, we focus on quadratizations that preserve the stability
properties of the original model, specifically dissipativity at given
equilibria. This preservation is desirable in many applications of
quadratization including reachability analysis and synthetic biology. We
establish the existence of dissipativity-preserving quadratizations, develop an
algorithm for their computation, and demonstrate it in several case studies.
