GATE EE 2014 Set 2 — Question 54

NAT+2 / -0MediumRouth-Hurwitz CriterionStability AnalysisControl Systems

Control Systems → Stability Analysis → Routh-Hurwitz Criterion

Last updated 5 September 2026

Question

G(s) = \frac{K}{s(s + 2)(s^2 + 2s + 2)}

1 + G(s)H(s) = 0 \Rightarrow 1 + \frac{K}{s(s + 2)(s^2 + 2s + 2)} = 0

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1 + G(s)H(s) = 0 \Rightarrow 1 + \frac{K}{s(s + 2)(s^2 + 2s + 2)} = 0

Row	Col 1	Col 2	Col 3
$s^4$	1	6	K
$s^3$	4	4	0
$s^2$	$\frac{4(6) - 1(4)}{4} = 5$	K	0
$s^1$	$\frac{5(4) - 4(K)}{5} = \frac{20 - 4K}{5}$	0	0
$s^0$	K	0	0

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