Scalable distributed and decentralized ${\mathcal{H}}_2$ controller synthesis for interconnected linear discrete-time systems

The current limitation in the synthesis of distributed ${\mathcal{H}}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed ${\mathcal{H}}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized ${\mathcal{H}}_2$ controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized ${\mathcal{H}}_2$ controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed ${\mathcal{H}}_2$ controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.