Exercise $4\mathrm{.}4($Inverted pendulum on cart system$)$ Consider the inverted pendulum sys$-$

tem with $(t)$ as output and $u(t)$ as input, described by the following transfer function

$(m{l}^2|))/(q$

where

$q=(M+m)(I+m{l}^2)-m{l}^2$

Let $M=0\mathrm{.}5kg,m=0\mathrm{.}5kg,I=0\mathrm{.}3m,I=0\mathrm{.}006kg*m^2,=0\mathrm{.}1N*\frac{s}{m}.$ Is the system

input$/$output stable?