Controllability Analysis of Two-Dimensional Systems Using 1D Approaches

Working with the 1D form of 2D systems is an alternative strategy to reduce the inherent complexity of 2D systems. To achieve the 1D form of 2D systems, different from the so-called WAM model, a new row (column) process was proposed recently. The controllability analysis of this new 1D form is explored in this note. Two new notions of controllability named WAM-controllability and directional controllability for the underlying 2D systems are defined. Corresponding conditions on the WAM-controllability and directional controllability are derived, which are particularly useful for the control problems of 2D systems via 1D framework. According to the presented directional controllability, a directional minimum energy control input is derived for 2D systems. A numerical example demonstrates the applicability of the presented analysis.