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GATE EE 2025 Set 1 — Question 62

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NAT+2 / -0EasyState-Space ModelState-Space AnalysisControl SystemsEigenvalues & EigenvectorsLinear AlgebraEngineering Mathematics

Control Systems → Linear Algebra → Eigenvalues & Eigenvectors

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Question

Consider the state-space modelx˙(t)=Ax(t)+Br(t),\dot{\mathbf{x}}(t) = A\mathbf{x}(t) + Br(t),y(t)=Cx(t)y(t) = C\mathbf{x}(t)where x(t),r(t),y(t)\mathbf{x}(t), r(t), y(t) are the state, input and output, respectively. The matrices A,B,CA, B, C are given belowA=[01−2−3],B=[01],C=[10]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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