The state equation of a second order system is $\dot{x}(t) = Ax(t)$, $x(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of A and $v_1$ and $v_2$ are the corresponding eigenvectors. For constants $\alpha_1$ and $\alpha_2$, the solution, $x(t)$, of the state equation is

$\sum_{i=1}^{2} \alpha_i e^{\lambda_i t} v_i$

$\sum_{i=1}^{2} \alpha_i e^{2\lambda_i t} v_i$

$\sum_{i=1}^{2} \alpha_i e^{3\lambda_i t} v_i$

$\sum_{i=1}^{2} \alpha_i e^{4\lambda_i t} v_i$

GATE 2023 Electronics & Communication Q43 — Electronics and Communication Engineerin

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Electronics and Communication Engineering · Control Systems - State Space Analysis

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Control Systems - State Space Analysis has appeared in GATE Electronics & Communication 5 times across 5 years (2019, 2023, 2024, 2025, 2026).

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state spaceeigenvalueseigenvectorssolutiondifferential equation