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Doctoral Thesis
DOI
10.11606/T.18.2016.tde-04082016-143234
Document
Author
Full name
Wendhel Raffa Coimbra
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Alberto, Luís Fernando Costa (President)
Amaral, Fabíolo Moraes
Brandão, Adilson José Vieira
Flauzino, Rogério Andrade
Gomes, Luciana Takata
Title in Portuguese
Extensão do princípio de invariância de LaSalle para sistemas periódicos e sistemas fuzzy
Keywords in Portuguese
Equações diferenciais
Princípio de invariância
Sincronização
Sistemas Fuzzy
Sistemas periódicos
Abstract in Portuguese
O princípio de invariância de LaSalle estuda o comportamento assintótico das soluções sem conhecer as soluções das equações diferenciais.Para isto,utiliza uma função auxiliar V usualmente chamada de função de Lyapunov. Este trabalho apresenta um princípio de invariância fuzzy e sua versão global para a classe de sistemas dinâmicos fuzzy descrito, via extensão de Zadeh,por equações diferenciais autônomas com incertezas na condição inicial.Ainda, apresentamos um princípio de invariância uniforme, no qual não se exige que a derivada da função de Lyapunov seja sempre definida negativa, para a classe de sistemas dinâmicos não lineares não autônomos que são descritos por um conjunto de equações diferenciais ordinárias periódicas. Aplicações para as duas classes de sistemas foram desenvolvidas.
Title in English
Extension of the LaSalle's invariance principle for periodic systems and fuzzy systems
Keywords in English
Differential equations
Fuzzy systems
Invariance principle
Periodic systems
Synchronization
Abstract in English
The LaSalle's invariance principle studies the asymptotic behavior of the solutions without requiring the knowledge of the solutions of differential equations. For this, it uses an auxiliary function V usually called Lyapunov function. This work proposes a fuzzy invariance principle and its global version for the class of fuzzy dynamic systems described, via Zadeh's extension, by autonomous ordinary differential equation with uncertainties in the initial condition. Moreover, we develop an uniform invariance principle, in which the derivative of the Lyapunov function is not required to be always negative definite, for the class of non autonomous non linear dynamical system described by a set of periodic ordinary differential equations. Applications for the two classes of systems are also developed.
 
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Wendhel.pdf (1.53 Mbytes)
Publishing Date
2016-08-05
 
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