GATE EE

Routh Hurwitz Stability

Control Systems

(Past Years Questions)

Marks 1

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A closed loop system has the characteristic equation given by $${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For...
GATE EE 2017 Set 1
A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$�...
GATE EE 2014 Set 3
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature ter...
GATE EE 2014 Set 1
The first two rows of Routh's tabulation of a third order equation are as follows $$$\left. {\matrix{ {{s^3}} \cr ...
GATE EE 2009
The system shown in the figure is ...
GATE EE 2007
None of the poles of a linear control system lie in the right half of $$s$$-plane. For a bounded input, the output of th...
GATE EE 1998
Closed loop stability implies that $$\left[ {1 + G\left( s \right)H\left( s \right)} \right]$$ has only ____________ in ...
GATE EE 1995
The number of positive real roots of the equation $${s^3} - 2s + 2 = 0$$ is __________.
GATE EE 1994
The closed loop system , of Figure, is stable if the transfer function $$T\left( s \right) = {{C\left( s \right)} \over ...
GATE EE 1994
For what range of $$K$$ is the following system (Figure) asymptotically stable Assume $$K \ge 0$$ ...
GATE EE 1992

Marks 2

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The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the compl...
GATE EE 2017 Set 2
Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which ...
GATE EE 2016 Set 1
The following discrete-time equations result from the numerical integration of the differential equations of an un-dampe...
GATE EE 2015 Set 2
A system with the open loop transfer function $$G\left( s \right) = {K \over {s\left( {s + 2} \right)\left( {{s^2} + 2s ...
GATE EE 2014 Set 2
For the given system, it is desired that the system be stable. The minimum value of $$\alpha $$ for this condition is __...
GATE EE 2014 Set 1
The feedback system shown below oscillates at $$2$$ rad/s when ...
GATE EE 2012
Figure shows a feedback system where $$K>0$$ The range of $$k$$ for which system is stable will by given by...
GATE EE 2008
If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {...
GATE EE 2007
The algebraic equation $$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$ $$F\left( s \right) = 0$$ ha...
GATE EE 2006
For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be
GATE EE 2004
A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {...
GATE EE 2004
The loop gain $$GH$$ of a closed loop system is given by the following expression $${K \over {s\left( {s + 2} \right)\le...
GATE EE 2003
The number of roots on the equation $$2{s^4} + {s^3} + 3{s^2} + 5s + 7 = 0$$ that lie in the right half of $$S$$ plane i...
GATE EE 1998
The system represented by the transfer function $$G\left( s \right) = {{{s^2} + 10s + 24} \over {{s^4} + 6{s^3} - 39{s^2...
GATE EE 1997
Determine whether the system given by the block diagram of Figure, is stable ...
GATE EE 1997

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