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

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.

Grantor dc:publisher

Universidade Federal do Rio de Janeiro

Year dc:date.issued

1971

Author dc:creator

• Fonseca, Luiz Gonzaga de Souza

Advisor dc:contributor.advisor

• Ribeiro, Demétrio Alonso

• Engenharia elétrica
• Sistemas não-lineares
• Equações diferenciais ordinárias
• Liapunov, Funções de

Statement dc:rights

• Acesso Aberto

Language dc:language

por

Handle dc:identifier.uri

http://hdl.handle.net/11422/3737

OAI identifier oai:identifier

oai:pantheon.ufrj.br:11422/3737