stability

The response of a discrete time system y[n] obeys the following relation: y[n] = (5/6)y[n-1] - (1/6)y[n – 2] + x[n]. The input to the system is x[n] = δ[n] – (1/3)δ[n – 1]. Which o...

Consider the unity negative feedback control system shown in the Figure. The value of gain K (>0) at which the given system will remain marginally stable is __. (Answer in integer)

Let $G(s) = \frac{1}{10s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below. Consider the...

Consider the polynomial p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 2s - 40. Let (L, I, R) be defined as follows. L is the number of roots of p(s) with negative real parts. I is the number...

Consider a system where $x_1(t)$, $x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given...

Consider a system where $x_1(t), x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given by...

Consider the polynomial $p(s)=s^5+7 s^4+3 s^3-33 s^2+2 s-40$. Let $(L, I, R)$ be defined as follows. $L$ is the number of roots of $p(s)$ with negative real parts. $I$ is the numbe...

For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2+3}{(z+\frac{1}{3})(z-\frac{1}{3})}$ which of the following statements is/are true?

Consider a unity negative feedback control system with forward path gain G(s) = K / ((s+1)(s+2)(s+3)) as shown. The impulse response of the closed-loop system decays faster than e⁻...

For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z - \frac{1}{3}\right)}$ which of the following statements is...

Consider an even polynomial p(s) given by $$p(s) = {s^4} + 5{s^2} + 4 + K$$ where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the im...

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function $G(s) = \frac{1}{s^2 + 3s + 2}$ where K > 0. Th...

A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of the following statements about the system is TRUE?

Which one of the following options correctly describes the locations of the roots of the equation s 4 + s 2 + 1 = 0 on the complex plane?

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as $$y\left[ n \ri...

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation. X: The sys...

The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is

The characteristic equation of an LTI system is given by F(s) = s 5 + 2s 4 +3s 3 + 6s 2 - 4s - 8 = 0.The number of roots that lie strictly in the left half s-plane is _____.

A plant transfer function is given as $$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\right)$$$ . When the plant operates in a unity feedback configu...

Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the imulse response h...

Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ with 'p' a positive real parameter. The maximum value of 'p' un...

A stable linear time invariant (LTI) system has a transfer function H(s) = $${1 \over {{s^2} + s - 6}}$$. To make this system casual it needs to be cascaded with another LTI system...

Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements. S1: The system is stable. S2: $${{h\l...

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$. The system is

A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

The transfer function of a discrete time LTI system is given by $$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$ Cons...

The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$

The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a unity feedback configuration, then the lead compensator that...

A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The...

For the polynomial P(s) = s 5 + s 4 + 2s 3 + 2s 2 + 3s + 15 , the number of roots which lie in the right half of the s-plane is

A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n \right] + \beta x\left[ {n - 1} \right].$$ The system is st...

The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {...

The open-loop transfer function of a unity feedback system is $$$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\right)}$$$ the range of 'k' for which the system is stable

The gain margin and the phase margin of a feedback system with G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ are

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship, $$y\left( n \right) = \left\{ {\matrix{ {x\le...

The characteristic polynomial of a system is q(s) = 2s 5 + s 4 + 4s 3 + 2s 2 + 2s + 1. The system is

If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is e...

The impulse response function of four linear system S1, S2, S3, S4 are given respectively by $${h_1}$$(t), = 1; $${h_2}$$(t), = U(t); $${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$; $${...

An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier

Introducing a resistor in the emitter of a common amplifier, stabilizes the dc operating point against variations in

A system described by the transfer function $$$H\left(s\right)=\frac1{s^3+\alpha s^2+ks+3}$$$ is stable. The constraints on $$\alpha$$ and k are,

The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are

The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. The gain margin of the system is

The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condi...

Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right. In the case of a linear time invariant system List - 1 (1) Poles in the right hal...

A system having an open loop transfer function $$G\left(s\right)=\frac{K\left(s+3\right)}{s\left(s^2+2s+2\right)}$$ is used in a control system with unity negative feedback. Using...

Tachometer feedback in a d.c. position control system enhances stability.

The poles of a continuous time oscillator are ___________.

If G(s) is a stable transfer function, then $$F\left(s\right)=\frac1{G\left(s\right)}$$ is always a stable transfer function.

The open loop frequency response of a system at two particular frequencies are given by: 1.2 $$\angle - 180^\circ $$ and 1.0 $$\angle - 190^\circ $$. The closed loop unity feedback...

The frequency compensation is used in OP-Amps to increase its___________

Match the following. GROUP-1 (A) Hartley (B) Wein-bridge (C) Crystal GROUP-2 (1) Low frequency oscillator (2) High frequency oscillator (3) Stable frequency oscillator (4) Relaxati...

Indicate whether the following statement is TRUE/FALSE: Give reason for your answer. If G(s) is a stable transfer function, then $$F\left( s \right) = {1 \over {G\left( s \right)}}...

If $$s^3+\;3s^2\;+\;4s\;+A\;=\;0$$ ,then all the roots of this equation are in the left half plane provided that

A linear discrete - time system has the characteristic equation, $${z^3} - 0.81\,\,z = 0.$$ The system

A linear second order single input continuous-time system is described by the following set of differential equations $$$\eqalign{ & \mathop {{x_1}}\limits^ \bullet \left( t \right...

An electromechanical closed-loop control system has the following characteristic equation $$s^3+6Ks^2+\left(K+2\right)s+8\;=\;0$$, where K is the forward gain of the system.The con...

Nyquist plot consider a feed back system where the OLTF is: $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}.$$ Determine the asymptote which the nyquist plot ap...

For the transfer function of a physical two-port network

The output of a system is given in difference equation form as $$y\left( k \right) = \,a\,\,y\left( {k - 1} \right) + x\left( k \right),$$ where $$x\left( k \right)$$ is the input....