GATE EC 2025 Set 1 Q26 — Control Systems

Let $G(s)=\frac{1}{10 s^{2}}$ 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.

1. There exists no controller of the form $M(s)=\frac{K_{I}}{s}$, where $K_{I}$ is a positive real number, such that the closed loop system is stable.
2. There exists at least one controller of the form $M(s)=K_{P}+s K_{D}$, where $K_{P}$ and $K_{D}$ are positive real numbers, such that the closed loop system is stable.

Which one of the following options is correct?