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Solving an output consensus problem in multi-agent systems is often hinderedby multiple time-variant delays. To address such fundamental problems overtime, we present a new optimal time-variant distributed control for linearlyperturbed multi-agent systems by involving an integral sliding mode controllerand a linear consensus scheme with constant wights under directed topology.Lyapunov-Krasovskii functionals along with linear matrix inequalities arejointly employed to demonstrate the associated closed-loop stability andconvergence features. Maximum delays for the communicating networks are alsoestimated by linear matrix inequalities. Synchronizing a network of lineartime-variant systems to the associated leader dynamics is additionally takeninto account by developing an optimization algorithm to find the constantcontrol gains.

Leader-Following Consensus of High-Order Perturbed Multi-agent Systems under Multiple Time-Varying Delays