Consider the following closed$-$loop system:

where $C(s)=K$ and $P(s)=\frac{1}{8\mathrm{.}01s+1}.$

Determine the smallest positive gain K such that the closed$-$loop system is stable and when $r(t)$ is a step signal of amplitude $1,$ we have $\underset{t}{lim}e(t)\frac{1}{11}$

Provide your answer with $1$ decimal point precision.