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Periodic event-triggered control (PETC) is a control strategy consisting of event-triggered control (ETC) and conventional periodic sampled-data control. By using event-triggering mechanisms (ETM) to periodically verify whether or not to transmit and compute the measured output, communication and computational datum are significantly reduced while still retaining a satisfactory performance. This paper investigates the PETC scheme of robust H ∞ filtering for a class of uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems, where the sample time is assumed to be a constant. To analyze the filtering problems of the PETC strategy, we present two frameworks based on perturbed linear and piecewise linear systems, to model filtering error systems. Sufficient conditions for the existence of a robust H ∞ filter are derived in the form of matrix inequalities (LMIs) under these two frameworks, respectively. Finally, a simulation example is used to testify to the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]