# Robust Almost Global Splay State Stabilization of Pulse Coupled Oscillators

## TL;DR

This paper presents a new method for stabilizing the evenly distributed phase configuration of pulse coupled oscillators, ensuring robustness and almost global stability through a novel Lyapunov approach.

## Contribution

It introduces a novel phase response function design and Lyapunov function for almost global stabilization of splay states in pulse coupled oscillators.

## Key findings

- Achieves almost global asymptotic stability of splay states
- Demonstrates robustness to frequency perturbations
- Validates effectiveness through an example

## Abstract

This technical note deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled oscillators is modeled as a hybrid system. The design of the phase response function is performed to achieve almost global asymptotic stability of a set wherein oscillators' phases are evenly distributed on the unit circle. To establish such a result, a novel Lyapunov function is proposed. Robustness with respect to frequency perturbation is assessed. Finally, the effectiveness of the proposed methodology is shown in an example.