# Routh Hurwitz Stability ยท Control Systems ยท GATE EE

Start Practice## Marks 1

GATE EE 2022

The open loop transfer function of a unity gain negative feedback system is given by $$G(s) = {k \over {{s^2} + 4s - 5}}$$. The range of k for which t...

GATE EE 2017 Set 1

A closed loop system has the characteristic equation given by
$${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, whi...

GATE EE 2014 Set 3

A single-input single-output feedback system has forward transfer function $$๐บ(๐ )$$ and feedback transfer function $$๐ป(๐ ).$$ It is given that $$\l...

GATE EE 2014 Set 1

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicate...

GATE EE 2009

The first two rows of Routh's tabulation of a third order equation are as follows
$$$\left. {\matrix{
{{s^3}} \cr
{{s^2}} \cr
} } \right|\...

GATE EE 2007

The system shown in the figure is
...

GATE EE 1998

None of the poles of a linear control system lie in the right half of $$s$$-plane. For a bounded input, the output of this system

GATE EE 1995

Closed loop stability implies that $$\left[ {1 + G\left( s \right)H\left( s \right)} \right]$$ has only ____________ in the left half of the $$s$$-pla...

GATE EE 1994

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 $$T\left( s \right) = {{C\left( s \right)} \over {R\left( s \right)}}$$ is stab...

GATE EE 1992

For what range of $$K$$ is the following system (Figure) asymptotically stable Assume $$K \ge 0$$
...

## Marks 2

GATE EE 2017 Set 2

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 complex $$s$$-plane is

GATE EE 2016 Set 1

Given the following polynomial equation $${s^3} + 5.5{s^2} + 8.5s + 3 = 0$$ the number of roots of the polynomial which have real parts strictly less ...

GATE EE 2015 Set 2

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator w...

GATE EE 2014 Set 2

A system with the open loop transfer function $$G\left( s \right) = {K \over {s\left( {s + 2} \right)\left( {{s^2} + 2s + 2} \right)}}$$ is connected ...

GATE EE 2014 Set 1

For the given system, it is desired that the system be stable. The minimum value of $$\alpha $$ for this condition is _________
...

GATE EE 2012

The feedback system shown below oscillates at $$2$$ rad/s when
...

GATE EE 2008

Figure shows a feedback system where $$K>0$$
The range of $$k$$ for which system is stable will by given by...

GATE EE 2007

If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {s + 8} \right)^2}$$ is to be a...

GATE EE 2006

The algebraic equation
$$F\left( s \right) = {s^5} - 3{s^4} + 5{s^3} - 7{s^2} + 4s + 20$$
$$F\left( s \right) = 0$$ has

GATE EE 2004

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( {1 - s} \right)} \over {\left( ...

GATE EE 2003

The loop gain $$GH$$ of a closed loop system is given by the following expression $${K \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$ The ...

GATE EE 1998

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 is:

GATE EE 1997

The system represented by the transfer function $$G\left( s \right) = {{{s^2} + 10s + 24} \over {{s^4} + 6{s^3} - 39{s^2} + 19s + 84}}$$ has . . . pol...

GATE EE 1997

Determine whether the system given by the block diagram of Figure, is stable
...