Real-Time 2-D-to-1-D Decomposition of Roesser Models via Sylvester Equation Transformation With Interval-Constrained Balanced Model Reduction

The complexity of 2-D systems makes them challenging to analyze and manage. Basic algebraic operations are more intricate in 2-D frameworks than in their 1-D counterparts. Standard 2-D systems can typically only be decomposed into 1-D subsystems if they are represented in a separable denominator form. This research introduces a novel transformation that facilitates the decomposition of a 2-D standard system into a diagonalized 2-D representation; this further enables its partitioning into two 1-D subsystems, bypassing the constraints of minimal rank decomposition criteria. The proposed framework (PF) retains the geometrical symmetry of the resultant 1-D submodels while maintaining balance across the submodels, making them suitable for model reduction in large-scale systems. Furthermore, a novel framework for model reduction is developed to address limitations in existing limited-interval (LI) methods, such as instability within the reduced system. The numerical findings indicate that the proposed transformations adequately diagonalize the standard 2-D system and ensure a stable reduced 2-D model.