Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

Autor(es)

Faria, Flavio A. ^[1] ; Silva, Geraldo N. ^[1] ; Oliveira, Vilma A. ^[2]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Paulo - Brazil

^[2] Univ Sao Paulo, Dept Engn Eletr, BR-13560970 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE; v. 44, n. 10, p. 1956-1969, OCT 1 2013.
• Citações Web of Science: 37

Resumo

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented. (AU)

• Processo FAPESP: 09/18643-0 - Controle ótimo de sistemas não lineares
• Beneficiário: Geraldo Nunes Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 09/16796-3 - Análise de estabilidade e projeto de controladores para sistemas fuzzy Takagi Sugeno usando funções de Lyapunov fuzzy
• Beneficiário: Flávio Andrade Faria
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado