A Decomposition Approach for a Class of Spatially Interconnected Systems of Finite Spatial Extent

This paper presents a decomposition approach for a class of spatially interconnected systems of finite extent obtained by discretizing partial differential equations including boundary conditions. Such finite extent systems can be modeled as an interconnection of identical subsystems communicating with their nearest neighbors resulting in a lattice-interconnection-topology. Recently the question has been raised whether this class of systems is decomposable. It is shown that these systems are decomposable with respect to a pattern matrix for which a construction law is presented, using the coefficients of the finite difference equation and taking the boundary conditions into account. By bringing the system into a decomposed form, several existing distributed analysis and synthesis techniques can be applied. This approached also helps to bridge the gap between spatially interconnected and multiagent systems. Finally, the approach is demonstrated with stability analysis on two numerical examples.