Extraction of 1-dimensional reaction-diffusion structure in SISO linear dynamical networks

In this paper, we propose a model order reduction method for SISO linear dynamical networks, where a large number of subsystems are interconnected according to a network. In this method, the structure of spatially one-dimensional reaction-diffusion that a SISO linear dynamical network has is extracted by way of Householder transformation ordering the state variables according to the distance from the source (i.e., an input) of the diffusion. Based on this structure, a model order reduction method with the diffusion structure of the system preserved is presented, which can be applied for large-scale systems. In addition, an easily-computable error bound via the proposed model reduction is derived.