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Fuzzy controller design based on stability criteria. (English) Zbl 1075.93522
The paper deals with stability of fuzzy controllers, namely Sugeno-Takagi ones. The latter are considered to be in the standardized form \[ f_i(y) = \frac {\sum _{\alpha }u_{\alpha }^{(i)}(y)\cdot a_{\alpha }^t(y)} {\sum _{\alpha } a_{\alpha }^t(y)} \] for each \(i\)-th output from the \(i\)-th rule (cf. the book [D. Driankov, H. Hellendoorn and M. Reinfrank, An introduction to fuzzy control, Springer-Verlag, Berlin (1993; Zbl 0789.93088)]).
The author finds a linearization formula for the above controller provided that specific (and quite common) assumptions for the membership functions are fulfilled. On the basis of this he proves existence of stability intervals for certain parameters of the fuzzy controller and accompanies the theory by a numerical example.
MSC:
93C42 Fuzzy control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
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