A Note on the Cross Gramian for Non-Symmetric Systems

By Himpe Christian and Ohlberger Mario
Working Paper (2015)

On Reduced Input-Output Dynamic Mode Decomposition

Working Paper (2017)

Himpe Christian, Benner Peter, and Mitchell Tim

Fast Low-Rank Empirical Cross Gramians

Working Paper (2017)

Himpe Christian, Leibner Tobias, Rave Stephan, and Saak Jens

emgr - The Empirical Gramian Framework

Working Paper (2018)

Himpe Christian

Cross-Gramian-Based Model Reduction: A Comparison

Working Paper (2016)

Himpe Christian and Ohlberger Mario

Parareal in Time Intermediate Targets Methods for Optimal Control Problems

International Series of Numerical Mathematics (2013)

Mohamed Kamel Riahi, Maday Yvon, and Julien salomon

The Empirical Cross Gramian for Parametrized Nonlinear Systems

Working Paper (2015)

Himpe Christian and Ohlberger Mario

Data-Driven Combined State and Parameter Reduction for Inverse Problems

Working Paper (2014)

Himpe Christian and Ohlberger Mario

Model Reduction for Complex Hyperbolic Networks

arXiv (2013)

Himpe Christian and Ohlberger Mario

LSD: A Fast Line Segment Detector with a False Detection Control

IEEE Transactions on Pattern Analysis and Machine Intelligence (2010)

Grompone von Gioi Rafael, Jakubowicz Jérémie, Morel Jean-Michel, and Randall Gregory

Abstract

The cross Gramian matrix is a tool for model reduction and system identification, but it is only applicable to square control systems. For symmetric systems the cross Gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to approximate a cross Gramian for non-symmetric and non-square systems. To illustrate this new non-symmetric cross Gramian, it is applied in the context of model order reduction.

See paper

Please cite the paper as follows:

Himpe C. and Ohlberger M. (2015) A Note on the Cross Gramian for Non-Symmetric Systems. Working Paper.

See paper