Abstract
In this paper, the optimal H2 model order reduction (MOR) problem for general MIMO linear time-invariant (LTI) systems is studied. The cross Gramian can provide the controllability and observability information of LTI systems at the same time and it thus is used to discuss the MOR problem. We first deal with the general MIMO system, obtaining a set of SISO subsystems. Then, the cost function related to each SISO subsystem is expressed via the cross Gramian. The orthogonality constraint of the cost function makes it is posed on the Stiefel manifold. Then, making full use of the geometry properties of this Stiefel manifold, we propose a feasible and effective iterative algorithm to solve the H2 minimization problem. In addition, we show that our algorithm is rigorously convergent. Finally, a couple of examples related to MIMO LTI systems demonstrate the effectiveness of our algorithm.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
