Consensus control and performance recovery of heterogeneous second-order multi-agent systems via two-time-scale separation approach

This paper addresses a two–time–scale separation-based redesign technique for achieving robust consensus and transient performance recovery in second-order multi-agent systems (MASs) subject to both unmodeled dynamics and external disturbances. The proposed protocol is developed for both undirected and directed information-exchange topologies. A key novelty of this work lies in its ability to not only guarantee consensus but also explicitly recover the nominal transient performance of the agents—a capability that is typically lost in the presence of uncertainties. Lyapunov stability analysis ensures that all MASs signals remain bounded, while the consensus tracking errors asymptotically converge to zero. Simulation results demonstrate the effectiveness and robustness of the proposed approach.