P$2.$ a$.$ Express the following $2^{nd}$ order Difference Equation in state$-$space format: $y(k+2)+3y(k+1)-\frac{1}{2}y(k)=u(k),$ where $u$ is input, $y$ is output, $k$ the counter of sampling time steps $T_s,$ and with $1$ actuator & $1$ sensor$.$

$4$ pts

b$.$ Obtain the Pulse Transfer Function $($i$.$e$.$ TF in the $z-$domain$)$ of the discretetime system described by the above Difference Equation.

$3$ pts

c$.$ Find its Partial Fraction Expansion by using Matlab's residue command. $3$ pts