  The cross gramian matrix is a tool for model reduction and system
identification, but it is only computable for 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.
