GATE EC 2020 Set 1 — Question 40

MCQ+2 / -0.67MediumState Variable ModelState-Space AnalysisControl Systems

Control Systems → State-Space Analysis → State Variable Model

Last updated 5 September 2026

Question

A circuit with current sources $i_1$, $i_2$, resistors $2 \Omega$, $1 \Omega$, inductor $0.5$ H, and capacitor $0.25$ F.

Your answer

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\frac{d}{dt} \begin{bmatrix} v \\ i \end{bmatrix} = \begin{bmatrix} -4 & 4 \\ -2 & -4 \end{bmatrix} \begin{bmatrix} v \\ i \end{bmatrix} + \begin{bmatrix} 0 & 4 \\ 4 & 0 \end{bmatrix} \begin{bmatrix} i_1 \\ i_2 \end{bmatrix}

\frac{d}{dt} \begin{bmatrix} v \\ i \end{bmatrix} = \begin{bmatrix} -4 & -4 \\ 2 & 4 \end{bmatrix} \begin{bmatrix} v \\ i \end{bmatrix} + \begin{bmatrix} 4 & 4 \\ 4 & 0 \end{bmatrix} \begin{bmatrix} i_1 \\ i_2 \end{bmatrix}

\frac{d}{dt} \begin{bmatrix} v \\ i \end{bmatrix} = \begin{bmatrix} 4 & -4 \\ -2 & -4 \end{bmatrix} \begin{bmatrix} v \\ i \end{bmatrix} + \begin{bmatrix} 0 & 4 \\ 4 & 0 \end{bmatrix} \begin{bmatrix} i_1 \\ i_2 \end{bmatrix}

\frac{d}{dt} \begin{bmatrix} v \\ i \end{bmatrix} = \begin{bmatrix} -4 & 4 \\ -2 & -4 \end{bmatrix} \begin{bmatrix} v \\ i \end{bmatrix} + \begin{bmatrix} 4 & 0 \\ 0 & 4 \end{bmatrix} \begin{bmatrix} i_1 \\ i_2 \end{bmatrix}

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