Defesa Pública da Dissertação de Mestrado do Engenheiro de Controle e Automação Leonardo Cabral
Data: 24/09/2021 - sexta-feira
A defesa será realizada através de videoconferência na plataforma Teams, pelo link:
Prof. Dr. Eugênio de Bona Castelan Neto - PPGEAS - UFSC
Profa. Dra. Lucíola Campestrini - PPGEE – UFRGS
Prof. Dr. Aurelio Tergolina Salton - PPGEE - UFRGS
Presidente da banca/Orientador: Prof. Dr. João Manoel Gomes da Silva Junior - PPGEE - UFRGS
Título da dissertação: "STABILITY ANALYSIS AND STABILIZATION OF DISCRETE-TIME PIECEWISE AFFINE SYSTEMS "
"This work addresses the problems of global stabilization and local stability analysis of discrete-time piecewise affine (PWA) systems.
To tackle the global stabilization problem, this work considers a PWA state feedback control law, a recently proposed implicit PWA representation and piecewise quadratic (PWQ) Lyapunov candidate functions. Through Finsler’s Lemma, congruence transfor- mations and some structural assumptions, quasi-LMI sufficient conditions to ensure the global exponential stability of the origin of the closed-loop PWA system are derived from the stability conditions. An algorithm is proposed to solve the quasi-LMI conditions and compute the stabilizing gains.
Regarding the problem of local stability analysis, this work proposes a method to test the local nonnegativity of PWQ functions using the implicit representation. This method is used to assess the local stability of the origin of PWA systems by considering PWQ Lyapunov candidate functions. Estimates of the Region of Attraction of the Origin (RAO) are obtained as level sets of the Lyapunov function. Approaches to obtain maximized estimates of the RAO are therefore discussed.
Keywords: Piecewise affine systems, stability and stabilization, piecewise quadratic Lyapunov functions, semidefinite programming."