GATE EC 2025 Set 1 Q43 — Control Systems

Consider a system where $x_{1}(t), x_{2}(t)$, and $x_{3}(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given by

$$\frac{d}{d t}\left[\begin{array}{l} x_{1}(t) \\ x_{2}(t) \\ x_{3}(t) \end{array}\right]=\left[\begin{array}{rrr} 2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 0 \end{array}\right]\left[\begin{array}{l} x_{1}(t) \\ x_{2}(t) \\ x_{3}(t) \end{array}\right]+\left[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}\right] u(t)$$

Which of the following statements is/are TRUE?