## Stability analysis of the discrete Takagi-Sugeno fuzzy model with time-varying consequent uncertainties.(English)Zbl 0993.93018

The study is concerned with the fuzzy dynamic model governed by “$$m$$” Takagi-Sugeno rules where the $$p$$th rule reads as follows $\begin{split} \text{- if }x(k)\text{ is }A_{p1}\text{ and }\dots\text{ and }x(k- n+1)\text{ is }A_{pn}\\ \text{then }x_p(k+ 1)= a_{p1} x(k)+\cdots+ a_{pm}x(k- n+1).\end{split}$ The linear part (subsystem) standing in the consequent part of the rule can be written in a matrix form $$A_px(k)$$, and this in turn leads to the output of the system governed by the expression $x(k+1)= \sum^m_{p=1} w_p(k) A_px(k)/ \sum^m_{p=1} w_p(k)$ (here the $$w_p(k)$$’s are the degrees of activation of the individual rules). It is assumed that the matrix $$A_p$$ comes with time-varying uncertainty (say $$A_p+\Delta A_p(k)$$) where the uncertainty matrices $$\Delta A_p(k)$$ are not known and their values are constrained to lie within known compact bounding sets. For this class of TS models, conditions for their global asymptotic stability are derived.

### MSC:

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

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