Fixed-time leader–follower consensus for second-order multi-agent systems: Variable exponent sliding mode control approach

This paper investigates the fixed-time leader–follower consensus (LFC) problem of second-order multi-agent systems (MASs) with bounded disturbance under directed interaction topology. First, a sliding mode manifold (SMM) with consensus errors–dependent variable exponential coefficient is given. Then, two sliding mode control (SMC) protocols are proposed. The proposed control protocols can eliminate the singularity, while guaranteeing the fixed-time reachability of the consensus errors to the sliding mode surface (SMS) and the fixed-time convergence of the consensus errors toward the origin along the SMS. Finally, the validity of the obtained methodology is confirmed by two simulation examples.