$1.-$ The open$-$loop control system transfer function is given:

$L(S)=\frac{K}{S(S+1)(S+2)},K=1,$ and $H(S)=1$

The Figure shows the Nyquist plot for the open$-$loop transfer function. Using the Nyquist criterion determine:

a$)$ Using the Nyquist criterion determine how many poles are on the right half of the plane for the closed$-$loop system. Is the system stable or unstable? Justify your answer. $(15\%)$

b$)$ What is the gain margin expressed in dB$?(15\%)$

c$)$ How much has to be increased the gain for making the system unstable? $(20\%)$