In this paper, stabilizability problems for discrete and continuous time linear systems with switching or polytopic uncertainties are dealt with. Both state feedback and full-information controllers are considered, possibly with an integral action. Several cases will be analyzed, depending on the control, the uncertainty and the presence of uncertainties in the input matrix. A complete overview of the stabilizability implications among these different cases will be given. (c) 2007 Elsevier Ltd. All rights reserved.