Then

$$\begin{aligned} \dot{\mathfrak{x}}(t) &= A\_8 \mathfrak{x}(t) + B\_8 \mathfrak{u}(t) \\ \mathfrak{y} &= C\_8 \mathfrak{x}(t) \end{aligned}$$

where M1 and M2 are fuzzy sets for z1ð Þt , M3 and M4 are fuzzy sets for z2ð Þt , and M5 and M6 are fuzzy sets for z3ð Þt .

According to the fuzzy rules, the Takagi-Sugeno fuzzy model of the EDF-100 distillation pilot plant is expressed in Eq. (23):

$$\begin{aligned} \dot{x}(t) &= \sum\_{i=1}^{8} h\_i(x(t)) (A\_i x(t) + B\_i u(t)) \\\\ y(t) &= \sum\_{i=1}^{8} h\_i(x(t)) (C\_i x(t)) \end{aligned} \tag{23}$$
