The authors deal with mode and parameter-dependent robust mixed ℋ₂/ℋ_∞ filtering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed ℋ₂/ℋ_∞ filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust ℋ₂ and ℋ_∞ performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.