Exploiting symmetry for the distributed control of spatially interconnected systems

This paper discusses distributed controller design and analysis for distributed systems with noncommutative symmetry groups. We show how recent results for designing control systems for spatially interconnected systems, based on semidefinite programming, are applicable to a much larger class of interconnection topologies. We also show how to exploit the form of the symmetry group to produce a hierarchy of decreasingly conservative analysis and synthesis conditions.