Decentralized controllers with integral action represent a large portion of multivariable controllers currently employed in the process industry. The integrity of these systems with respect to loop failures has been relatively well researched. In particular, important results have been found with respect to the relative gain array (RGA). However, less has been done on the treatment of the integrity of uncertain systems. This paper considers the integrity conditions of uncertain systems with norm-bounded uncertainties, and extends four existing integrity conditions to these uncertain systems. These are: integral stabilizable (IS), integral controllable (IC), integral controllable with integrity (ICI), and decentralized integral controllability (DIC). For the first three, necessary and sufficient conditions are derived. For the DIC condition, a sufficient condition has been derived. These conditions impose a limit on the norm of the allowed perturbations, below which the closed-loop system is guaranteed to maintain integrity. (C) 2011 Elsevier Ltd. All rights reserved.