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Abstract
Repetitive controllers (RCs) are linear control structures based on the internal model principle. This control strategy is known for its ability to control periodic reference signals, even if these signals have many harmonic components. Despite being a solution that results in a good performance, several parameters of the repetitive controller need to be correctly tuned to guarantee its stability. Among these parameters, one that has high impact on the system performance and stability is the finite impulse response (FIR) filter, which is usually used to increase the stability domain of RC-based controllers. In this context, this paper presents a complete tutorial for designing the zero-phase FIR filter, which is often used to stabilize control systems that use RC-based controllers. In addition, this paper presents a Matlab® application developed for performing the stability analysis of RC systems and designing its FIR filter. Simulation and experimental results of a shunt active power filter are used to validate the algorithm and the Matlab® application.

Abstract
Introduction and Objectives: Obstructive sleep apnea (OSA) is a prevalent sleep condition which is very heterogeneous although not formally characterized as such, resulting in missed or delayed diagnosis. Cluster analysis has been used in different clinical domains, particularly within sleep disorders. We aim to understand OSA heterogeneity and provide a variety of cluster visualizations to communicate the information clearly and efficiently.Materials and Methods: We applied an extension of k-means to be used in categorical variables: k -modes, to identify OSA patients' groups, based on demographic, physical examination, clinical his-tory, and comorbidities characterization variables (n = 40) obtained from a derivation and validation cohorts (211 and 53, respectively) from the northern region of Portugal. Missing values were imputed with k-nearest neighbours (k-NN) and a chi-square test was held for feature selection.Results: Thirteen variables were inserted in phenotypes, resulting in the following three clus-ters: Cluster 1, middle-aged males reporting witnessed apneas and high alcohol consumption before sleep; Cluster 2, middle-aged women with increased neck circumference (NC), non -repairing sleep and morning headaches; and Cluster 3, obese elderly males with increased NC, witnessed apneas and alcohol consumption. Patients from the validation cohort assigned to dif-ferent clusters showed similar proportions when compared with the derivation cohort, for mild (C1: 56 vs 75%, P = 0.230; C2: 61 vs 75%, P = 0.128; C3: 45 vs 48%, P = 0.831), moderate (C1: 24 vs 25%; C2: 20 vs 25%; C3: 25 vs 19%) and severe (C1: 20 vs 0%; C2: 18 vs 0%; C3: 29 vs 33%) levels. Therefore, the allocation supported the validation of the obtained clusters.Conclusions: Our findings suggest different OSA patients' groups, creating the need to rethink these patients' stereotypical baseline characteristics.(c) 2021 Sociedade Portuguesa de Pneumologia. Published by Elsevier Espana, S.L.U. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).