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This paper deals with the problem of robust H∞ filtering for linear discrete-time state-space models with uncertain time-varying parameters. The parameters enter affinely into the state-space model matrices, and their admissible values and variations are assumed to belong to given intervals. A method is derived for designing a linear stationary asymptotically stable filter with a prescribed H∞ performance, in spite of large parameter uncertainty. The proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a Lyapunov function with quadratic dependence on the parameters. The filter design is given in terms of linear matrix inequalities.