Scalable distributed and decentralized H2 controller synthesis for interconnected linear discrete-time systems
Abstract
The current limitation in the synthesis of distributed H2 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 H2 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 H2 controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized H2 controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed H2 controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.