Nonlinear Model Reduction in the Loewner Framework

Abstract

We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense.