$6\mathrm{.}19$ Consider the continuous$-$time state equation in Problem $4\mathrm{.}2$ and its discretized equations in Problem $4\mathrm{.}3$ with sampling period $T=1$ and $.$ Discuss controllability and observability of the discretized equations.

$4\mathrm{.}2$ Use two different methods to find the unit$-$step response of

$x^{}=\left[\begin{array}{ccc}0& 1& -2\end{array}\right]$

$-2x+\left[\begin{array}{c}1\end{array}\right]$

$1u$

$y=\left[\begin{array}{cc}2& 3\end{array}\right]x$

$4\mathrm{.}3$ Discretize the state equation in Problem $4\mathrm{.}2$ for $T=1$ and $T=.$