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This study is concerned with the problem of H∞ filtering for two-dimensional (2-D) Markovian jump systems with delays varying in given ranges. The 2-D jump systems under consideration are described by the well-known Fornasini-Marchesini models with state delays. Different from conventional techniques using the discrete Jensen inequality which guides various delay-dependent conditions for delayed systems, a precise upper estimation is presented via a rigorous treatment of the lower bound for a linear combination of positive-definite matrices with reciprocal coefficients. By carefully selecting components of an augmented vector with algebraic constraints, a delay-range-dependent approach is proposed for the design of H∞ filters such that the filtering error system is stochastically stable and has a prescribed H∞ disturbance attenuation level. A numerical example is provided to illustrate the effectiveness of the developed method.