Control Design for Topology-Independent Stability of Interconnected Systems

In this paper we present a method for synthesis of decentralized controllers for multiple identical systems interconnected on a graph. We develop a synthesis procedure for controllers which will stabilize the system for any graph topology satisfying given degree bounds, independent of the size of the graph. 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. We also show how these results may be extended to construct partially decentralized controllers which receive measurements from their neighbors. We illustrate the results via an example of a power distribution network.