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This paper is concerned with network-based static output feedback tracking control for a class of nonlinear systems that can not be stabilized by a static output feedback controller without a time-delay, but can be stabilized by a delayed static output feedback controller. For such systems, network-induced delay is intentionally introduced in the feedback loop to produce a stable and satisfactory tracking control. The nonlinear network-based control system is represented by an asynchronous T-S fuzzy system with an interval time-varying sawtooth delay due to sample-and-hold behaviors and network-induced delays. A new discontinuous complete Lyapunov-Krasovskii functional, which makes use of the lower bound of network-induced delays, the sawtooth delay and its upper bound, is constructed to derive a delay-dependent criterion on H∞ tracking performance analysis. Since routine relaxation methods in traditional T-S fuzzy systems can not be employed to reduce the conservatism of the stability criterion, a new relaxation method is proposed by using asynchronous constraints on fuzzy membership functions to introduce some free-weighting matrices. Based on the feasibility of the derived criterion, a particle swarm optimization algorithm is presented to search the minimum H∞ tracking performance and static output feedback gains. An illustrative example is provided to show the effectiveness of the proposed method.