GATE 2014 EC (EC4) – Question 56

Control Systems · State Variable Model and Solution of State Equation · 2 marks · Multiple choice

Find the state-transition matrix for $\dot{\mathbf x}=\begin{pmatrix}0&1\\0&0\end{pmatrix}\mathbf x$.

$\begin{pmatrix}t&1\\1&0\end{pmatrix}$
$\begin{pmatrix}1&0\\t&1\end{pmatrix}$
$\begin{pmatrix}0&1\\1&t\end{pmatrix}$
$\begin{pmatrix}1&t\\0&1\end{pmatrix}$

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Correct answer: (D) $\begin{pmatrix}1&t\\0&1\end{pmatrix}$

Explanation

The state matrix is A=[[0,1],[0,0]], and A²=0. Therefore the matrix-exponential series terminates:e^(At)=I+At. The state transition matrix is **[[1,t],[0,1]],D**. It equals the identity at t=0as required.