This paper proposes a multi-agent system approach to robust formation control design of multi-UAV for powerline inspection applications. A backstepping multi-agent sliding mode control (BMA-SMC) method that is equipped with radial basis function neural network (RBFNN) estimator of wind disturbances is developed for the multi-UAV system to ensure precise and robust tracking of the powerline cables and towers. Combined with the developed RBFNN estimator, the proposed BMA-SMC thus provides a robust formation control scheme that is capable of mitigating wind disturbance from the environment when tracking the reference powerline cables and towers. An event-triggered control execution scheme is also proposed to ensure efficient utilization of each UAV's computational and communication resources when implementing the developed formation control scheme. Simulation results of multi-UAV formation movements when tracking conventional powerline cable network configurations are reported to illustrate the effectiveness of the proposed robust multi-UAV control scheme.