A Unified Software Framework for Empirical Gramians

Abstract

A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying 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 provide 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 (MIMO) systems.

Preprint

Cited by in corpus (7)

• Optimal PMU Placement for Power System Dynamic State Estimation by Using Empirical Observability Gramian
• emgr - The Empirical Gramian Framework
• Hierarchical Approximate Proper Orthogonal Decomposition
• Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance
• Cross-Gramian-Based Combined State and Parameter Reduction for Large-Scale Control Systems
• A Note on the Cross Gramian for Non-Symmetric Systems
• Structured interpolation for multivariate transfer functions of quadratic-bilinear systems