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This paper presents new non-fragile Hinfin filter design methods for linear discrete-time systems. The filter to be designed is assumed to be with additive gain variations, which reflect the FWL effects in filter digital implementations. A notion of structured vertex separator is proposed to approach the problem, and exploited to develop sufficient conditions for the non-fragile Hinfin filter design in terms of solutions to a set of linear matrix inequalities (LMIs). Moreover, to reduce the design conservativeness, the slack variable method is adopted to realize the decoupling between the Lyapunov matrix and the system dynamic matrix. The designs render the augmented system asymptotically stable and guarantee the Hinfin attenuation level less than a prescribed level. A numerical example is given to illustrate the design methods and the design benefits.