A Note on the Cross Gramian for Non-Symmetric Systems

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.

Himpe C. and Ohlberger M. (2016) A Note on the Cross Gramian for Non-Symmetric Systems. System Science and Control Engineering, 4, 199--208.