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GATE EE 2026 Set 1 — Question 52

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MCQ+2 / -0.67MediumTransfer Function from StatesState-Space AnalysisControl Systems

Control Systems → State-Space Analysis → Transfer Function from States

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Question

A system is characterized by the following state equation and output equation (uu: input, x\mathbf{x}: state vector, yy: output)x˙=[ab−a0]x+[10]u\dot{\mathbf{x}} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix} \mathbf{x} + \begin{bmatrix} 1 \\ 0 \end{bmatrix} uy=[12]xy = \begin{bmatrix} 1 & 2 \end{bmatrix} \mathbf{x}What are the values of aa and bb for which the poles of the transfer function are at −2+j3-2 + j3 and −2−j3-2 - j3 ?
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