In this paper, we consider the problem of set-membership identification of multiple-input multiple output (MIMO) linear models when both input and output measurements are affected by bounded additive noise. Firstly, we propose a general formulation that allows the user to take into account possible a-priori information on the structure of the MIMO model to be identified. Then, we formulate the problem in terms of a suitable polynomial optimization problem that is solved by means of a convex relaxation approach. To show the effectiveness of the proposed approach, we test the original MIMO identification algorithm on a simulation example, as well as on a set of input-output experimental data, collected on a multiple-input multiple-output electronic process simulator. (C) 2018 Elsevier Ltd. All rights reserved.