Observer-Based Stabilization for Linear Multi-Agent Dynamical Systems Using Generalized Frequency Variables

TL;DR

This paper develops observer-based controllers for linear multi-agent systems using generalized frequency variables, ensuring stability and enabling independent design of observers and controllers.

Contribution

It introduces a novel separation principle for networked systems and provides necessary controllability and observability conditions based on agent and network properties.

Findings

Networked controllers and observers ensure stability of system state and estimation error.

Separation principle allows independent design of observers and controllers.

Necessary conditions for controllability and observability are derived from agent and network structure.

Abstract

We address the conditions and design of controllers and observers for homogeneous networks of linear MIMO agents. We develop networked controllers and observers that ensure the stability of both the system state and the estimation error, leveraging the concept of generalized frequency variables. A separation principle for networks is then established, showing that the observer and controller can be designed independently and combined to achieve a stable output feedback. Our results are illustrated via a highly unstable, oscillatory network of locally actuated pendulums on carts. Finally, necessary conditions for controllability and observability -- derived from agent properties and network structure -- are established and discussed.