Abstract: The fractional control theory was used to study delay of network control system， and an optimal fractionalorder PIλDμ network delay controller was designed. The control effects of the optimal PIλDμ and optimal PID controller with fixed and random network delay were compared and simulated. The results showed that both fractionalorder and integerorder controllers could achieve satisfactory results for the network control system of integerorder， but the overshoot， rising time and accommodation time of step response of fractionalorder PIλDμ controller were smaller than those of the integerorder one， and it was proved that optimal fractionalorder controller possessed more capacity to deal with network delay.

Key words: network control system, network delay, fractional calculus, optimal control, fractionalorder PIλDμ controller