Transformation of Two-Dimensional Roesser Model Into Two-Dimensional Decoupled Model: Application to Model Reduction via Balanced Framework

Abstract

Two transformations are presented in this research; the first approach takes a generic two-dimensional (2-D) framework and transforms it into a diagonalized 2-D framework without resorting to minimal rank-decomposition criteria. Afterward, it converts the diagonalized system into two subsystems (i.e., one-dimensional (1-D) cascaded systems). Moreover, the proposed transformation retains the symmetrical structure of the two decomposed subsystems. Likewise, the second transformation converts 1-D submodels to the balanced structure used for model reduction operations. The proposed model reduction approach efficiently performs the model reduction task on a given 2-D diagonalized model by utilizing optimal Hankel norm approximation. The numerical results demonstrate that the proposed transformations efficiently convert the standard 2-D framework to a diagonalized model form and develop a stable reduced-order model.