Abstract
This paper focuses on the Hilbert–Schmidt-Hankel-norm ( norm) optimal model order reduction (MOR) of large-scale multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems on the Stiefel manifold. First, a cost function is constructed in regard to the norm. By introducing the orthogonality constraints, the norm optimal MOR problem is converted into an unconstrained minimisation problem on the Stiefel manifold. We derive the Riemannian gradient of the cost function on the Stiefel manifold. The MOR algorithm is developed associated with the Riemannian conjugate gradient method. Global convergence is guaranteed with mild conditions. Finally, the effectiveness of the proposed method is illustrated by two numerical examples.
Acknowledgements
The authors would like to thank the editors and the reviewers for their valuable comments and constructive suggestions that have helped us improve the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).