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A novel characterization of bumpless transfer among alternative controllers, both in continuous and discrete time, is introduced. The bumpless transfer problem is to design a compensation scheme guaranteeing an L2 (respectively l2) bound on the mismatch, after the switching time from one controller to another between the actual plant output and a particular target plant output that corresponds to an ideal response. Minimization of the gain from initial plant state mismatch to L2 (respectively, l2) plant output mismatch provides improved transients. A solution to the bumpless transfer problem is given, based on the L2 anti-windup solution described in Teel and Kapoor (1997) and Grimm et al. (2003), both for plants without input saturation and for plants with input saturation. The solution guarantees anti-windup features in the latter case. The proposed methodology is shown to perform well on a simulation example.