Routh Hurwitz Stability · Control Systems · GATE EE

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, which one of the following conditions should be satisfied?

A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$𝐻(𝑠).$$ It is given that $$\left| {G\left( s \right)H\left( s \right)} \right| < 1.$$ Which of the following is true about the stability of the system?

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 indicates the presence of

The first two rows of Routh's tabulation of a third order equation are as follows $$$\left. {\matrix{ {{s^3}} \cr {{s^2}} \cr } } \right|\matrix{ 2 & 2 \cr 4 & 4 \cr } $$$
this means there are

The system shown in the figure is

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

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

The number of positive real roots of the equation $${s^3} - 2s + 2 = 0$$ is __________.

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 stable.

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

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

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 than $$-1$$ is _____________.

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $$𝑥$$ and $$𝑦.$$ The integration time step is $$h.$$ $$${{{x_{k + 1}} - {x_k}} \over h} = {y_k},\,\,\,\,\,{{{y_{k + 1}} - {y_k}} \over h} = {x_k}$$$

For this discrete-time system, which one of the following statements is TRUE?

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 in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of $$K$$ is ________.

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

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

Figure shows a feedback system where $$K>0$$

The range of $$k$$ for which system is stable will by given by

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 adjusted to induce a sustained oscillation then

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

A unity feedback system, having an open loop gain becomes stable when $$G\left( s \right)H\left( s \right) = {{K\left( {1 - s} \right)} \over {\left( {1 + s} \right)}}$$

For the equation, $${s^3} - 4{s^2} + s + 6 = 0$$ the number of roots in the left half of $$s$$ plane will be

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 value of $$K$$ for which the system just becomes unstable is

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:

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

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 . . . pole $$(s)$$ in the right-half $$s$$-plane.