This paper presents a technique for model reduction of spatially distributed systems. It is applicable to systems with dynamics that evolve continuously in time, but whose spatial structure is inherently discrete. The technique relies on linear matrix inequality (LMI) based synthesis results developed for control design of spatially interconnected systems. A key property which is exploited in the derivation of synthesis results is spatial invariance, which means that the system dynamics remain unchanged with translation in spatial coordinates. Such systems can be modelled by linear fractional transformations (LFTs) on spatial and temporal variables. The results in this paper are presented in terms of LMIs, making the reduction problem computationally attractive.

This paper presents a new approach for model reduction of distributed state space systems. It is applicable to spatio-temporal systems that evolve in discrete time over a finite interval; the spatial structure of these systems is also inherently discrete. The main contribution of this paper is that it allows the underlying system dynamics to be shift variant with respect to spatial or temporal variables. The simplification technique presented in this paper relies on control synthesis results developed for heterogeneous systems. It is stated in terms of inequalities on finite dimensional space which can be immediately converted to linear matrix inequalities (LMIs), making the reduction problem readily amenable to computation.