# Distributed Synthesis of Local Controllers for Networked Systems with Arbitrary Interconnection Topologies

## TL;DR

This paper presents a method for designing distributed controllers for networked systems to ensure dissipativity, enabling local synthesis without full network knowledge and supporting plug-and-play operations in microgrids.

## Contribution

It introduces a novel distributed dissipativity analysis and controller synthesis approach that is scalable and compositional for arbitrary interconnection topologies.

## Key findings

- Distributed analysis guarantees network dissipativity.
- Local controllers ensure overall system stability.
- Method supports plug-and-play in microgrids.

## Abstract

We consider the problem of designing distributed controllers to guarantee dissipativity of a networked system comprised of dynamically coupled subsystems. We require that the control synthesis is carried out locally at the subsystem-level, without explicit knowledge of the dynamics of other subsystems in the network. We solve this problem in two steps. First, we provide distributed subsystem-level dissipativity analysis conditions whose feasibility is sufficient to guarantee dissipativity of the networked system. We then use these conditions to synthesize controllers locally at the subsystem-level, using only the knowledge of the dynamics of that subsystem, and limited information about the dissipativity of the subsystems to which it is dynamically coupled. We show that the subsystem-level controllers synthesized in this manner are sufficient to guarantee dissipativity of the networked dynamical system. We also provide an approach to make this synthesis compositional, that is, when a new subsystem is added to an existing network, only the dynamics of the new subsystem, and information about the dissipativity of the subsystems in the existing network to which it is coupled are used to design a controller for the new subsystem, while guaranteeing dissipativity of the networked system including the new subsystem. Finally, we demonstrate the application of this synthesis in enabling plug-and-play operations of generators in a microgrid by extending our results to networked switched systems.