The goal of this paper is to present a different approach to the analysis of the absolute stability of Lurie type systems in the single-input-single-output (SISO) case using robust control theory. The proposed technique enables the design of controllers via ${\mathcal{H}}_{\infty }$ mixed-sensitivity (S/KS/T), where, besides making the system absolutely stable, the performance problem can also be solved. In addition, it is also demonstrated that it is possible to make use of this new approach in time-delay Lurie type systems. Thus, through a new methodology, this work paves the way to the study of the absolute stability of multiple-inputs-multiple-outputs (MIMO) systems, aiming at a better generalization of the theory and enabling applications in other areas, such as neural networks. Examples, numerical simulations and application in Chua’s circuit are given to illustrate the results.

For preventing health complications and reducing the strain on healthcare systems, early identification of diseases is imperative. In this context, artificial intelligence has become increasingly prominent in the field of medicine, offering essential support for disease diagnosis. This article introduces an algorithm that builds upon an earlier methodology to assess biosignals acquired through cardiopulmonary exercise testing (CPET) for identifying metabolic syndrome (MS), heart failure (HF), and healthy individuals (H). Leveraging support vector machine (SVM) technology, a well-known machine learning classification method, in combination with wavelet transforms for feature extraction, the algorithm takes an innovative approach. The model was trained on CPET data from 45 participants, including 15 with MS, 15 with HF, and 15 healthy controls. For binary classification tasks, the SVM with a polynomial kernel and 5-level wavelet transform (SVM-POL-BW5) outperformed similar methods described in the literature. Moreover, one of the main contributions of this study is the development of a multi-class classification algorithm using the SVM employing a linear kernel and 3-level wavelet transforms (SVM-LIN-MW3), reaching an average accuracy of 95%. In conclusion, the application of SVM-based algorithms combined with wavelet transforms to analyze CPET data shows promise in diagnosing various diseases, highlighting their adaptability and broader potential applications in healthcare.