Autor(es)

Gomes, Izabella O. ; Tognetti, Eduardo S. ; Oliveira, Ricardo C. L. F. ; Peres, Pedro L. D. ; IEEE

• Tipo de documento: Artigo Científico
• Fonte: 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2019-01-01.

Resumo

This paper addresses the problem of nonquadratic stability and estimation of domains of attraction for continuous time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. The T-S fuzzy model is obtained by the sector nonlinearity approach and represents exactly the nonlinear system in a compact set of the state-space. Sufficient linear matrix inequality (LMI) conditions to access local stability are obtained using homogeneous polynomially parameter-dependent Lyapunov functions and slack variables introduced through the Finsler's Lemma. The time-derivatives of the membership functions are handled by means of a polytopic representation of the gradient of the membership functions. As a technical novelty, whenever possible, the nonlinear terms of the gradient are handled through a Taylor series expansion, avoiding the definition of new (generally overbounded) uncertain parameters that increase the numerical complexity. Finally, a numerical example is presented to show the superiority of the approach in terms of estimating larger domains of attraction when compared with previous methods from the literature. (AU)

• Processo FAPESP: 17/18785-5 - Desigualdades Matriciais Lineares Dependentes de Parâmetros Aplicadas à Análise de Estabilidade e à Síntese de Controladores e Filtros para Sistemas Dinâmicos com Incertezas
• Beneficiário: Pedro Luis Dias Peres
• Modalidade de apoio: Auxílio à Pesquisa - Regular