A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

This paper addresses the time-varying output formation-containment control problem for homogeneous high-order linear Multi-Agent Systems (MASs). In this context, a PID-like output-feedback control strategy is proposed capable to guarantee that all followers reach and maintain a time-varying formation reference behaviour, as imposed by the multiple leaders, while keeping a prescribed offset with respect to it. Moreover, the proposed approach allows dealing with both communication impairments and external disturbances acting on agents dynamics. The asymptotic stability of the closed-loop MAS is analytically proved by means of a Lyapunov–Krasovskii approach. Stability conditions are expressed as a feasibility problem with Linear Matrix Inequalities constraints, whose solution provides the proper tuning of the robust PID control gains. Extensive numerical analysis confirms the theoretical framework and discloses the effectiveness of the proposed approach in ensuring the output time-varying formation-containment.