The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE.

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

For a unity feedback control system with the forward path transfer function

$$G(s) = {K \over {s\left( {s + 2} \right)}}$$

The peak resonant magnitude M_r of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.

The state equation and the output equation of a control system are given below:

$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$

$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$

The transfer function representation of the system is