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Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions |
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| Authors: | Flávio A. Faria Geraldo N. Silva Vilma A. Oliveira |
| Affiliation: | 1. Instituto de Biociências Letras e Ciências Exatas , UNESP – Univ Estadual Paulista , 15054-000, S?o José do Rio Preto, S?o Paulo , Brazil flaviof15@yahoo.com.br;3. Instituto de Biociências Letras e Ciências Exatas , UNESP – Univ Estadual Paulista , 15054-000, S?o José do Rio Preto, S?o Paulo , Brazil;4. Departamento de Engenharia Elétrica , Universidade de S?o Paulo , 13560-970, S?o Carlos, S?o Paulo , Brazil |
| 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. |
| Keywords: | TS fuzzy systems fuzzy Lyapunov functions stability analysis PDC fuzzy controllers linear matrix inequalities |