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This study addresses the l2−l∞ filter design issue for fuzzy Markov stochastic systems with sensor failures and packet dropouts. A more general failure model is used for Markov systems to better describe the sensor failures, and the packet dropouts are assumed to obey a series of Bernoulli processes which are formed into a diagonal matrix. Sufficient condition is established to guarantee that the filtering error system is stochastically stable and achieves the given l2−l∞ performance. The parameters of the filter are then derived by solving linear matrix inequalities. Simulation results are given to demonstrate the usefulness and availability of the proposed method. [ABSTRACT FROM AUTHOR]