This paper considers H∞ tracking control for a class of network-based T-S fuzzy systems with available asynchronous constraints on membership functions. Using a fuzzy controller associated with available sampled-data of both premise variables and feedback states, the network-based control system is equivalent to an asynchronous T-S fuzzy system with an interval time-varying sawtooth delay. Notice that the routine relaxation methods in traditional T-S fuzzy systems can not be used for stability analysis and controller design of the asynchronous fuzzy system since common product terms of membership functions can not be grouped. Instead, a new relaxation method is proposed by using asynchronous constraints on fuzzy membership functions to introduce some free weighting matrices. By using the proposed relaxation method and a new discontinuous Lyapunov-Krasovskii functional, some criteria on H∞ tracking performance analysis and controller design are derived. Compared with the existing results, the derived criteria are of less conservatism and allow the existence of a network-based fuzzy controller with different gains, which can ensure a better H∞ tracking performance. The effectiveness of the proposed method is illustrated by an example.