GATE 2025 EE – Question 62
Consider the state-space model
$\dot{\boldsymbol x}(t)=A\boldsymbol x(t)+Br(t)$,
$y(t)=C\boldsymbol x(t)$
where $\boldsymbol x(t)$, $r(t)$, $y(t)$ are the state, input and output, respectively. The matrices $A,B,C$ are given below
$$A=\begin{bmatrix}0&1\\-2&-3\end{bmatrix},\ B=\begin{bmatrix}0\\1\end{bmatrix},\ C=\begin{bmatrix}1&0\end{bmatrix}$$
The sum of the magnitudes of the poles is ______________ (round off to nearest integer).
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Show answer and explanation
Correct answer: 3
Explanation
The poles are the eigenvalues: $\det(sI-A)=s^2+3s+2=(s+1)(s+2)$, so $s=-1,-2$. The sum of magnitudes is $1+2=3$.