GATE Electrical 2026 | Question: 42

Question

A system is characterized by the following state equation and output equation ( $u$ : input, $\mathbf{X}$ : state vector, $y$ : output)

\[
\begin{array}{c}
\dot{\mathbf{x}}=\left[\begin{array}{cc}
a & b \\
-a & 0
\end{array}\right] \mathbf{x}+\left[\begin{array}{l}
1 \\
0
\end{array}\right] u \\
y=\left[\begin{array}{ll}
1 & 2
\end{array}\right] \mathbf{x}
\end{array}
\]
What are the values of $a$ and $b$ for which the poles of the transfer function are at $-2+\mathrm{j} 3$ and $-2-\mathrm{j} 3$ ?

• A. $a=4, b=3.25$
• B. $a=-4, b=3.25$
• C. $a=4, b=-3.25$
• D. $a=-4, b=-3.25$