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This paper considers a class of spatially interconnected systems formed by ladder circuits using two-dimensional systems theory. The individual circuits in this class are described by hybrid (continuous/discrete) linear differential/difference equations in time (continuous) and spatial (discrete) variables and therefore have a two-dimensional systems structure. This paper shows that a ladder circuit model and models for 2-D dynamics have a well defined equivalence property and hence analysis tools can be transferred between them. Also the mechanism for transforming one to the other is established.

Characterization of a class of spatially interconnected systems (ladder circuits) using two-dimensional systems theory