The characteristic equation of an LTI system is given by
F(s) = s⁵ + 2s⁴ +3s³ + 6s² - 4s - 8 = 0.The number of roots that lie strictly in the left half s-plane is _____.

For the system shown in the figure, s = –2.75 lies on the root locus if K is_____.

Consider the Bode plot shown in the figure. Assume that all the poles and zeroes are real-valued. The value of f_H - f_L (in Hz) is ______.

The transfer function of a first-order controller is given as $${G_c}(s) = {{K\left( {s + a} \right)} \over {s + b}}$$

where k, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is