# Consensus analysis of systems with time-varying interactions : An event-triggered approach

## TL;DR

This paper analyzes how multi-agent systems with time-varying interactions can achieve consensus using event-triggered control, demonstrating exponential convergence with dynamic triggers and extending results to switching topologies.

## Contribution

It introduces a novel event-triggered control approach for systems with time-varying graphs, including switching topologies, and proves exponential consensus under dynamic triggers.

## Key findings

- Dynamic trigger functions ensure exponential convergence.
- Static triggers lead to convergence within a bounded region.
- Results are validated through simulations.

## Abstract

We present consensus analysis of systems with single integrator dynamics interacting via time-varying graphs under the event-triggered control paradigm. Event-triggered control sparsifies the control applied, thus reducing the control effort expended. Initially, we consider a multi-agent system with persistently exciting interactions and study the behaviour under the application of event-triggered control with two types of trigger functions- static and dynamic trigger.We show that while in the case of static trigger, the edge-states converge to a ball around the origin, the dynamic trigger function forces the states to reach consensus exponentially. Finally, we extend these results to a more general setting where we consider switching topologies. We show that similar results can be obtained for agents interacting via switching topologies and validate our results by means of simulations.