  Solving an output consensus problem in multi-agent systems is often hindered
by multiple time-variant delays. To address such fundamental problems over
time, we present a new optimal time-variant distributed control for linearly
perturbed multi-agent systems by involving an integral sliding mode controller
and a linear consensus scheme with constant wights under directed topology.
Lyapunov-Krasovskii functionals along with linear matrix inequalities are
jointly employed to demonstrate the associated closed-loop stability and
convergence features. Maximum delays for the communicating networks are also
estimated by linear matrix inequalities. Synchronizing a network of linear
time-variant systems to the associated leader dynamics is additionally taken
into account by developing an optimization algorithm to find the constant
control gains.
