Novas condições de estabilidade de sistemas não lineares utilizando funções de Lyapunov fuzzy

• Ano de defesa: 2015
• Autor(a) principal: Guedes, Jarbas Antônio [UNESP]
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Controle automatico; Teoria do controle não-linear; Desigualdades (Matemática); Nonlinear control theory
• Link de acesso: http://hdl.handle.net/11449/136109; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/03-03-2016/000859488.pdf

This thesis proposes two new stability conditions regarding nonlinear systems des- cribed by Takagi-Sugeno (TS) fuzzy models, based on Fuzzy Lyapunov Functions (FLF). The first result is based on the hyper-rectangle defined by the closed set of the time deriva- tives of the membership functions of TS fuzzy systems, and is described by a set of Linear Matrix Inequalities (LMIs). The second result is based on the obtention of a polytope composed by the intersection of the hyperplane of the time derivatives of the membership functions with the hyper-rectangle. Two proposed theorems offer necessary and sufficient conditions for this stability problem. Examples, using the MATLAB software, illustrate the numerical results and show that the hyper-rectangle allows the reduction of the con- servatism of the stability analysis considering similar results available in the literature and with the polytope it is possible to obtain the same results with a smaller computati- onal time. Therefore, the proposed methods generalize previous results about asymptotic stability available in the literature, for nonlinear systems described by TS fuzzy models, based on FLF