Fully Distributed Prescribed-Time Robust Consensus Tracking for General Linear Multi-Agent Systems with Uncertainties and Disturbances

This paper investigates prescribed-time (Pre-T) robust consensus tracking for general linear multi-agent systems (LMASs) subject to uncertainties and disturbances. Such uncertainties and disturbances, which are common in practical systems, often hinder the achievement of Pre-T convergence. To address this challenge, a class of time-varying scaling functions is introduced as part of the observer and controller gains, ensuring robust consensus tracking of the closed-loop system within the prescribed time while mitigating the adverse effects of disturbances on tracking performance. Building on these scaling functions, a novel distributed Pre-T observer is developed to accurately estimate the leader's state for each follower at an arbitrarily chosen prescribed time $T_1$. The proposed Pre-T observer relies solely on local interaction information among neighboring followers and does not require global knowledge of the entire LMAS. Using the estimated leader's state, a Pre-T controller with some robustness terms is designed for each follower to counteract the negative impacts of system uncertainties and external disturbances. Furthermore, sufficient conditions for the existence of feasible control parameters are derived to guarantee that Pre-T robust consensus tracking with a specified $H_{\infty }$ performance index is achieved at a prescribed settling time $T_2$ and maintained thereafter. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.