Control Systems - Stability Analysis

Consider the unity negative feedback control system shown in the Figure. The value of gain K (>0) at which the given system will remain marginally stable is __. (Answer in integer)

Let $G(s) = \frac{1}{10s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below. Consider the following statements. (i) There exists...

Consider the polynomial p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 2s - 40. Let (L, I, R) be defined as follows. L is the number of roots of p(s) with negative real parts. I is the number of roots of p(s) that are purely imagina...