The finite-time boundness(FTB) analysis and finite-time ??∞ controller design for the affine switched system are discussed based on the average dwell-time method. Several definitions about FTB and robust ??∞ controllers are presented, based on which, the sufficient conditions and the designed method of the ??_∞ controller ensuring the FTB for the affine switched system are proposed. The obtained results are in the form of the linear matrix inequality(LMI). Finally a numerical example illustrates the correctness and effectiveness of the proposed method.