Sparse Representations of Dynamical Networks: A Coprime Factorization Approach

TL;DR

This paper introduces a coprime factorization approach for sparse dynamical networks, enabling structured representations and distributed control implementations for both discrete- and continuous-time systems.

Contribution

It develops a framework for shifting between sparsity-preserving factorizations, facilitating distributed control design for linear time-invariant networks.

Findings

Provides tractable methods for factorization-based network analysis

Enables distributed stabilization and control implementations

Extends techniques to both discrete- and continuous-time systems

Abstract

We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the structure of their component subsystems' interconnection. In doing so, we provide tractable means of shifting between different types of sparsity-preserving representations and we show how to employ these factorizations to obtain distributed implementations for stabilizing and possibly stable controllers. By formulating all these results for both discrete- and continuous-time systems, we develop specialized distributed implementations that, up to this point, were only available for networks modeled as discrete-time systems.