# Leader-Following Consensus of High-Order Perturbed Multi-agent Systems under Multiple Time-Varying Delays

## TL;DR

This paper develops a novel distributed control method for high-order perturbed multi-agent systems with multiple time-varying delays, ensuring stability and consensus through Lyapunov-Krasovskii functionals and linear matrix inequalities.

## Contribution

It introduces an optimal control scheme combining sliding mode control and linear consensus for delayed multi-agent systems, with delay estimation and leader synchronization.

## Key findings

- Ensures stability and convergence of multi-agent systems with delays.
- Provides delay bounds via linear matrix inequalities.
- Achieves leader-following consensus with optimized control gains.

## Abstract

Solving an output consensus problem in multi-agent systems is often hindered by multiple time-variant delays. To address such fundamental problems over time, we present a new optimal time-variant distributed control for linearly perturbed multi-agent systems by involving an integral sliding mode controller and a linear consensus scheme with constant wights under directed topology. Lyapunov-Krasovskii functionals along with linear matrix inequalities are jointly employed to demonstrate the associated closed-loop stability and convergence features. Maximum delays for the communicating networks are also estimated by linear matrix inequalities. Synchronizing a network of linear time-variant systems to the associated leader dynamics is additionally taken into account by developing an optimization algorithm to find the constant control gains.