A Unified Software Framework for Empirical Gramians

Abstract EN

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system.

Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method.

This work introduces a unified software framework supplying routines for six types of empirical Gramians.

The Gramian types will be discussed and applied in a model reduction framework for multiple-input multiple-output systems.