Simplification of spatially distributed systems

Abstract

A technique for the simplification of spatially distributed systems is presented. This technique relies on linear matrix inequality (LMI) based reduction results originally developed for the simplification of uncertain and multi-dimensional systems. The original results are applicable to systems that can be modelled by linear fractional transformations (LFTs) on structured operator sets whose elements are assumed to be temporal variables. In the paper, the original LFT results are extended to systems written as LFTs on spatial variables as well as on temporal variables. The main technical difference in the derivation of the new reduction results is a relaxation of standard causality requirements (or equivalently stability requirements), which in turn leads to a relaxation of the constraints to the relevant LMI solutions.