Cross-Gramian-Based Dominant Subspaces
For researchers in model reduction of linear systems, this work offers an incremental extension of an existing method by incorporating the cross Gramian, with no quantitative performance gains reported.
The paper extends the dominant subspace projection model reduction method to use the cross Gramian for linear systems, providing an a-priori error indicator and efficient computation, with numerical examples demonstrating the approach.
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.