A Note on the Cross Gramian for Non-Symmetric Systems

By Himpe Christian and Ohlberger Mario
Working Paper (2015)

Cross-Gramian-Based Dominant Subspaces

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On Reduced Input-Output Dynamic Mode Decomposition

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Fast Low-Rank Empirical Cross Gramians

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International Series of Numerical Mathematics (2013)

Mohamed Kamel Riahi, Maday Yvon, and Julien salomon

The Empirical Cross Gramian for Parametrized Nonlinear Systems

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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.

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Please cite the paper as follows:

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

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