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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 $$\multline \text{- if }x(k)\text{ is }A_{p1}\text{ and }\dots\text{ and }x(k- n+1)\text{ is }A_{pn}\\ \text{then }x_p(k+ 1)= a_{p1} x(k)+\cdots+ a_{pm}x(k- n+1).\endmultline$$ 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 systems 93D20 Asymptotic stability of control systems
Full Text:
References:
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