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this paper proposes a method for robust H∞ filtering for discrete systems with polytopic uncertainties. The parameter uncertainties considered in this paper are assumed to be of polytopic type. A new structured polynomially parameterdependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. The filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.