# Explicit Characterization of Performance of a Class of Networked Linear Control Systems

## TL;DR

This paper provides a unified framework to analyze the steady-state variance performance of networked linear control systems, linking it to Laplacian eigenvalues and offering insights into connectivity thresholds and scalability.

## Contribution

It introduces a general method to characterize network performance via Laplacian eigenvalues, extending previous results to arbitrary nodal dynamics and observer-based feedback.

## Key findings

- Performance expressed as sum over Laplacian eigenvalues
- Derived bounds and scaling laws for network performance
- Extended methodology to observer-based and composite networks

## Abstract

We show that the steady-state variance as a performance measure for a class of networked linear control systems is expressible as the summation of a rational function over the Laplacian eigenvalues of the network graph. Moreover, we characterize the role of connectivity thresholds for the feedback (and observer) gain design of these networks. We use our framework to derive bounds and scaling laws for the performance of the dynamical network. Our approach generalizes and unifies the previous results on the performance measure of these networks for the case of arbitrary nodal dynamics. We bring extensions of our methodology for the case of decentralized observer-based output feedback as well as a class of composite networks. Numerous examples support our theoretical contributions.