Example: Consider the linearized model of the

inverted pendulum, described by $=01$

$15\mathrm{.}79$

$0$

$$

$+$

$0$

$1\mathrm{.}46$

$$

$$

$=$

$0\mathrm{.}5$

m

$,$

$$

$=100$

g and initial conditions

$$

$$

$0$

$=$

$$

$($

$0$

$)$

$$

$($

$0$

$)$

$$

$=$

$1$

$0$

$$

$$ It is desired to stabilize the system using fuzzy

rules

i$.$ IF

$$ is positive AND

$$ is positive THEN

$$ is

negative

ii$.$ IF

$$ is negative AND

$$ is negative THEN

$$ is

positive