Forty Plus Years of Model Reduction and Still Learning

The approximation of complex dynamical systems models by reduced order models has been considered an important research problem for over four decades, not only in the field of control, but also in economics, image processing, circuit analysis, statistical mechanics, aircraft structures, and more recently in hybrid energy systems, to name just a sampling of fields. In this paper, we provide an overview of the development of balanced truncation and interpolation approaches for reducing linear and non-linear dynamical systems models for the purpose of control analysis and design.