This note deals with the problem of controlling an uncertain multivariable plant in the presence of input saturation via switching among a finite family of controllers having a generalized anti-windup architecture. The problem is addressed within the multi-model unfalsified adaptive switching control framework. It is shown that proper definitions of fictitious references and test functionals allow to prove stability of the overall switching scheme, provided that at least one controller in the finite family is stabilizing. The satisfiability of this assumption is discussed and simulation results are reported. (C) 2017 Elsevier Ltd. All rights reserved.