Design of MIMO Lur'e oscillators via dominant system theory with application in multi-agent rhythm synchronization

TL;DR

This paper introduces a novel control design framework for MIMO Lur'e oscillators using extended dominant system theory, enabling independent design of controllers and observers, with applications in multi-agent rhythm synchronization.

Contribution

It extends dominant system theory to state-dependent rates and develops a separation principle for Lur'e oscillator design, facilitating multi-agent synchronization.

Findings

Successful synchronization of heterogeneous agents into phase-locked rhythms

Derivation of LMIs for controller and observer design

Application to multi-agent systems demonstrating practical effectiveness

Abstract

This paper presents a new design framework for dynamic output-feedback controllers for Lur'e oscillation in a multiple-input multiple-output setting. We first revisit and extend dominant system theory to state-dependent rates, with the goal of deriving conditions based on linear matrix inequalities. Then, we introduce a separation principle for Lur'e oscillator design, which allows for the independent design of a state-feedback oscillator and an observer. Our proposed control synthesis is demonstrated through the rhythm synchronization in multi-agent systems, illustrating how networks of stable, heterogeneous linear agents can be driven into phase-locked rhythmic behavior.