Problem $1$: $($State space method$)$ Consider the plant $G(s)=\frac{20(s-5)}{s(s+1{)}^2}$ for the following questions:

Derive the state$-$space representation for the plant.

Design a full$-$state feedback controller; specifically, determine its feedback gains so that the closed$-$loop poles at $s_{1,2}=-5+-j7,s_3=-3.$

Derive the state$-$space representation and the transfer function of the close$-$loop digital controlled system.