Domínios de estabilidade assintótica: sua determinação utilizando o segundo Método de Liapunov

• Ano de defesa: 1971
• Autor(a) principal: Fonseca, Luiz Gonzaga de Souza
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio de Janeiro; Brasil; Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia; Programa de Pós-Graduação em Engenharia de Sistemas e Computação; UFRJ
• Palavras-chave em Português: Engenharia elétrica; Sistemas não-lineares; Equações diferenciais ordinárias; Liapunov, Funções de; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO; CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA
• Link de acesso: http://hdl.handle.net/11422/3737

Presents some methods to determine the domains of asyntotical stability of the trivial solution of first-order, non-linear, differential equations when Liapnov's second (direct) method is used. The first three chapters are introductory and present an historical review, the use of quadratic forms as Liapunov's functions, and a physical interpretation of the mathematical treatment. Chapter 4 presents an application of Linear System Theory to autonomous systems, and the determination of the ellipticals and sphericals domains of stability. A logical procedure of the criterium is also presented. The following chapters introduce the Schultz Gibson's and Zubov's methods. The first uses a line integral of the gradient of Liapunov's function. The second uses a partial differential equation that, as long as it has a closed-form solution, allows the determination os the exact domain of asyntotic stability. All the concepts considered essentials are introduced · in order to obtain a self- contained work as such as possible.