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On the global stability of Takagi-Sugeno general model. (English) Zbl 0959.93037

The authors study the stability of Takagi-Sugeno fuzzy models governed by a system of “if-then” rules of the form \[ \text{if }x\text{ is }A_1\text{ and }x'\text{ is }A_2\text{ and }\dots\text{ and } x^{(n- 1)}\text{ is }A_n\text{ then }d{\mathbf x}/dt= {\mathbf a}_0+ A{\mathbf x}+ B{\mathbf u}. \] The fuzzy sets standing in the condition part of the rules are described by triangular membership functions, \({\mathbf x}\) denotes a state vector and \({\mathbf u}\) stands for the input vector. The constant part \(({\mathbf a}_0)\) is nonzero. For this type of fuzzy model, one discusses its stability and an asymptotic stability theorem is given. The paper includes some illustrative examples.

MSC:

93C42 Fuzzy control/observation systems
93D20 Asymptotic stability in control theory
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