TY - JOUR
T1 - H2 optimal reduced models of general MIMO LTI systems via the cross Gramian on the Stiefel manifold
AU - Jiang, Yaolin
AU - Xu, Kangli
N1 - Publisher Copyright:
© 2017 The Franklin Institute
PY - 2017/5
Y1 - 2017/5
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85015070737
U2 - 10.1016/j.jfranklin.2017.02.019
DO - 10.1016/j.jfranklin.2017.02.019
M3 - 文章
AN - SCOPUS:85015070737
SN - 0016-0032
VL - 354
SP - 3210
EP - 3224
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 8
ER -