Google Meet link: https://meet.google.com/bgt-oqys-gme
This presentation offers novel computer algebraic approaches and numerical techniques to analyze and quantify certain behavioral aspects of a wide class of nonlinear uncertain models, which span different scientific areas, e.g., bio-engineering (fermentation processes models), transportation (highway models), aerospace (satellite motion or temperature dynamics), epidemiology (disease spread models), etc. The arising questions related to the dynamic behavior of a system can be often traced back to constrained (typically nonlinear) optimization problems or feasibility tests, which are still difficult to solve. These nonlinear problems are often solved using the sum of squares (SOS) methodology, which relies on the Positivstellensatz (PS) and a quadratic polynomial decomposition technique. In the past few years, we have demonstrated that a polytopic approach with Finsler's lemma and the affine annihilators together with the efficient numerical methodology of the linear fractional representation (LFR) has multiple attracting features compared to the SOS approaches, especially in the local analysis of rational models. Furthermore, we proposed systematic workflows to compute the domain of attraction, the induced L2-norm, or a passivating output function for a wide class of nonlinear systems. Although these techniques mainly focus on the dissipativity-related analysis or controller synthesis, we expect that they can answer further important questions in the field of nonlinear systems theory.