Topology independent controller design for networked systems

In this paper we present a method for synthesis of decentralized controllers for systems interconnected on a graph. We develop a synthesis procedure which will achieve a specified level of performance for any graph topology satisfying given degree bounds, independent of the size of the graph. We also give an analysis condition which gives an upper bound on the performance achieved for all such topologies. The methods reduce to computation via semidefinite programming, and the size of the resulting optimization problem does not grow with the size of the graph.