Estabilidade em tempo finito de sistemas lineares com parâmetros variantes no tempo: abordagem aleatória

• Ano de defesa: 2024
• Autor(a) principal: Nguemo, Mauricelle Sonya Kana
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Tecnológica Federal do Paraná; Cornelio Procopio; Brasil; Programa de Pós-Graduação em Engenharia Elétrica; UTFPR
• Palavras-chave em Português: Engenharia elétrica; Sistemas lineares; Finito; Electric engineering; Linear systems; CNPQ::ENGENHARIAS; Engenharia Elétrica
• Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/34865

The aim of this work is to develop a new strategy to check the finite-time stability of linear parameter-varying (LPV) systems. By applying the classical Lyapunov method, sufficient conditions are derived to ensure finite-time stability for larger classes of time-varying systems, extending beyond the scope of existing results. The concept of contractive stability in T-steps adapted to LPV systems has been developed. As the optimized contraction problem demands a prohibitive computational burden even for small values of T, a randomized approach is applied to solve it. The robust finite-time contractive stability of LPV systems in T-steps is tested in terms of a feasibility problem involving linear matrix inequalities (LMIs). The randomized approach is able to ensure the feasibility of the optimization problem with a high degree of probability, providing a test algorithm that guarantees the contractive stability of the system in T-steps within a finite time. The use of the Mayne’s algorithm, a specific case of Kalman filter, for the identification of MR damper has proved very beneficial, resulting in the system identification with an error of less than 0.001%. A controller was designed and adapted to an MR damper system coupled to a shaking table to experimentally validate the stability theories discussed in this work, resulting in data obtained from real-time experiments.