This paper proposes a new discretization technique with constant sampling time for time-invariant systems with uncertain parameters belonging to a polytopic domain. The aim is to provide an equivalent discrete-time representation of the continuous-time system whose ℋ2 guaranteed cost is an upper bound for the ℋ2 worst case norm of the original system. The resulting discrete-time model is described in terms of homogeneous polynomial matrices obtained by Taylor series expansion of degree ℓ. The discretization residual error, associated to the chosen approximation degree, is represented by additive norm-bounded uncertain terms. As a second contribution, new linear matrix inequality (LMI) relaxations for the computation of ℋ2 guaranteed costs for discrete-time systems with polynomial dependence on the uncertain parameter and additive norm-bounded uncertainties are proposed. 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