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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE; v. 44, n. 10, p. 1956-1969, OCT 1 2013.
• Web of Science Citations: 37

Abstract

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)

• FAPESP's process: 09/18643-0 - Optimal control of nonlinear systems
• Grantee: Geraldo Nunes Silva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 09/16796-3 - Stability analysis and control designs for Takagi Sugeno fuzzy systems with fuzzy Lyapunov functions
• Grantee: Flávio Andrade Faria
• Support Opportunities: Scholarships in Brazil - Post-Doctoral