Distributed Robust Finite-Time PID control for the leader-following consensus of uncertain Multi-Agent Systems with communication delay

Abstract

In this paper, the robust finite-time leader-following consensus problem for homogeneous uncertain linear Multi-Agent Systems (MASs) in the presence of time-varying communication delays is addressed and solved via a distributed time-delay PID-like control strategy. To analytically prove the robust finite-time stability of the resulting delayed neutral-type closed-loop MAS, we leverage both the descriptor transformation and the Lyapunov-Krasovskii theory. Delay-dependent finite-time stability conditions are expressed as a set of Linear Matrix Inequalities (LMIs), whose solutions allows obtaining both the weighted ℒ2 gain and the state trajectories bound. Numerical results confirm the theoretical derivation and the effectiveness of the proposed approach in guaranteeing that each agent converges towards the leader reference behavior in a finite-time interval despite the presence of both time-varying delays and external disturbances.