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This paper presents a controller design method using a blending method based on a common Lyapunov function for the induced L2-norm problem for switched linear parameter varying (LPV) systems with slowly-varying parameters. The parameter region is divided into two overlapped subsets, and Lyapunov existence conditions are proposed in terms of linear matrix inequalities (LMIs) for each subset. Based on each Lyapunov function in each subset, the blending method is used to construct a blended Lyapunov function for the whole parameter set. The proposed method is applied to an F-16 aircraft longitudinal model and simulation result demonstrate the effectiveness of the approach.