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

Area of Science:

• Control Systems Engineering
• Systems Analysis
• Applied Mathematics

Background:

• Two-dimensional (2-D) systems present significant analytical and management challenges due to their inherent complexity.
• Standard 2-D systems often require separable denominator representations for decomposition into 1-D subsystems.
• Existing model reduction techniques, like limited-interval (LI) methods, can suffer from instability in the reduced system.

Purpose of the Study:

• To introduce a novel transformation for decomposing standard 2-D systems into a diagonalized 2-D representation.
• To enable the partitioning of 2-D systems into two 1-D subsystems, overcoming minimal rank decomposition constraints.
• To develop an advanced framework for model reduction addressing limitations of current LI methods.

Main Methods:

• A novel transformation is proposed to diagonalize standard 2-D systems.
• The transformation facilitates the decomposition into two balanced 1-D submodels, preserving geometrical symmetry.
• A new model reduction framework is developed, specifically targeting instability issues in reduced systems.

Main Results:

• The proposed transformation successfully diagonalizes standard 2-D systems.
• The decomposition yields two geometrically symmetric and balanced 1-D submodels.
• Numerical results confirm the stability of the reduced 2-D model obtained through the new framework.

Conclusions:

• The novel transformation effectively simplifies 2-D systems by enabling decomposition into manageable 1-D subsystems.
• The proposed model reduction framework enhances stability and suitability for large-scale applications.
• This research offers a robust method for analyzing and reducing complex 2-D systems.