$4\mathrm{.}13$Consider the second$-$order system

G$($s$)=1$s$2+2$s$+1.$

We would like to add a transfer function of the form Dc$($s$)=$K$($s$+$a$)$K$($s$+$b$)$ in series with G$($s$)$ in a unity feedback structure.

Ignoring stability for the moment, what are the constraints on K$,$a$,$ and b so the system is Type $1?$

What are the constraints placed on K$,$a$,$ and b so the system is both stable and Type $1?$

What are the constraints on a and b so the system is both Type $1$ and remains stable for every positive value for K$?$