# Distributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus

arXiv: https://arxiv.org/abs/1310.8620 · HTML: https://mlsanity.com/paper/1310.8620/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2013.

## Built on by (most cited first, 1 of 1)

- [Continuous-Depth Neural Models for Dynamic Graph Prediction](https://mlsanity.com/paper/2106.11581/) (2021)

## Abstract (arXiv)

This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.