A linear switched system with bounded unknown inputs is considered in this paper. The study of the controlled distinguishability (or discernibility) property of the operating modes of the system is addressed. This property ensures the existence of a control input that generates different output signals of the modes regardless of the initial state vector and the unknown inputs. Such control inputs are called discerning controls. The robustness problem of the discerning controls with respect to the unknown inputs is analyzed, namely: under which conditions does a discerning control of the unknown-input-free modes remains a discerning control for the perturbed modes? To solve this problem, the existence of a quantifier measuring the size of the unknown inputs that discerning controls of the unknown-input-free modes have to be robust to in order to remain discerning controls for the perturbed modes is shown. In addition to this robustness result, an algorithm is proposed to design discerning controls for perturbed modes. Finally, from this input design procedure it is proven that when bounded unknown inputs are considered, there is an equivalence between controlled distinguishability of the unknown-input-free modes and that of the perturbed modes. (C) 2018 Elsevier Ltd. All rights reserved.