The complete Nyquist plot of the open-loop transfer function $G(s) H(s)$ of a feedback control system is shown in the figure.

If $G(s) H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is

A unity feedback system that uses proportional - integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters $K_p$ and $K_I$ The maximum value of $K_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally - stable (rounded off to three decimal places) is $\_\_\_\_$

The loop transfer function of a negative feedback system is

$$ G(s) H(s)=\frac{K(s+11)}{s(s+2)(s+8)} $$

The value of $K$, for which system is marginally stable, is $\_\_\_\_$ .

Consider p(s) = s³ + $${a_2}$$s² + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is