Defesa Pública da Tese de Doutorado do Mestre em Engenharia Elétrica LEONARDO CABRAL, de acordo com os termos do convênio de co-tutela entre a UFRGS e a Université Paris-Saclay, França.
Data: 19/12/2025 – sexta-feira
Horário: 9:00 (Brasil), 13:00 (França)
A defesa será realizada no formato híbrido, presencial na Sala 301-A do Instituto Eletrotécnico da UFRGS – Av. Osvaldo Arannha 103, Porto Alegre-RS, Brasil e pela plataforma Microsoft Teams, com acesso pelo link:
https://teams.microsoft.com/l/meetup-join/19%3ameeting_NTY1MmQ5Y2YtNTA5YS00MDU1LWE5NzMtNDdiOWEzMzE1YTQ2%40thread.v2/0?context=%7b%22Tid%22%3a%22b34c1d55-a43e-4a20-9218-a1a42eab149a%22%2c%22Oid%22%3a%22e3d79e3e-b1a6-4c93-96e2-2ef9680a14b7%22%7d
Banca Examinadora:
Prof. Dr. Gerard Scorletti – Laboratoire Ampère – CNRS – École Centrale de Lyon, França (Relator francês)
Prof. Dr. Daniel Ferreira Coutinho – Departamento de Automação e Sistemas (DAS) – UFSC (Relator brasileiro)
Profa. Dra. Isabelle Queinnec – Laboratoire d’Analyse et d’Architecture des Systèmes – CNRS – Toulouse University, França
Prof. Dr. Antoine Girard – Laboratoire des Signaux et Systèmes – CentraleSupélec – Gif-sur-Yvette, França
Profa. Dra. Lucíola Campestrini – PPGEE – UFRGS
Presidente da Banca: Prof. Dr. João Manoel Gomes da Silva Junior – PPGEE – UFRGS (Orientador brasileiro)
Prof. Dr. Giorgio Valmorbida – CentraleSupélec – Université Paris-Saclay, França (Orientador francês)
Títle: “ANALYSIS OF PIECEWISE AFFINE SYSTEMS WITH A RAMP-BASED IMPLICIT REPRESENTATION”
Abstract:
“Piecewise Affine (PWA) systems are a class of nonlinear dynamical systems characterized by affine dynamics defined over a partition of the state space. Their importance stems from the ability to model a wide range of nonlinear behaviors. However, stability analysis of such systems is challenging due to the combinatorial complexity associated with the number of partitions and the possible transitions between sets along the trajectories. As a result, existing stability analysis techniques are usually restricted to systems with a small number of states and partition sets. This thesis addresses the stability analysis of the origin of PWA systems through an implicit representation based on ramp functions. First, we develop conditions based on linear matrix inequalities and copositive matrices
to verify the nonnegativity of piecewise quadratic functions, both globally and locally, using convex optimization tools. Such conditions allow solving Lyapunov inequalities, which provide certificates of exponential stability of the origin. Moreover, in the context of local stability, the level sets of piecewise quadratic Lyapunov functions can be used to estimate the region of attraction of the origin. The proposed approach not only reduces the conservatism inherent to existing techniques but also presents better computational scalability, enabling the analysis of higher-dimensional systems and systems with more partition sets. The advantages of the method are demonstrated through numerical examples in both continuous-time and discrete-time.
Keywords: Piecewise affine systems, Exponential stability, Piecewise quadratic Lyapunov functions, Semidefinite programming, Copositive matrices.”
