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Higher Study | Control Systems | Stability Analysis

A system is defined as marginally stable when
The first element of each of the rows of the Routh-Hurwitz stability test showed the signs as follows: Row I II III IV V Sign + - - + -  Consider the following statements: 1. The system has three roots in the right-half of s-plane. 2. The system has three roots in the left-half of s-plane. 3. The system is stable. 4. The system is unstable. Which of the above statements about the system are correct?
Which of the following is NOT the advantage of Routh-Hurwitz criterion of control systems?
Consider the following statements related to stability of the control system : 1. Poles in right half-plane (rhp) yield pure exponential decaying natural response. 2. If poles of multiplicity greater than one are present on the imaginary axis, then the system is marginally stable, 3. If one pole is present in right-half plane, the system is unstable. 4. A system is stable if the natural response approaches zero as time approaches  infinity. Which of the above statements is/are not correct ?  
Which of the following systems are marginally stable? 1. e-2t sin 3t u(t) 2. t u(t) 3. u(t) 4. sin ωt u(t)
Consider the following statements: Routh-Hurwitz criterion gives A. Absolute stability B. The number of roots lying on the right half of the s-plane. C. The gain margin and phase margin. Which of these statement are correct?
The stability of a system which approaches the origin as time tends to infinity is termed as
Consider the following statements with respect to Routh-Hurwitz criterion: 1. It can be used to determine relative stability 2. It is valid only for real coefficients of the characteristic equation. 3. It is applicable only for non-linear systems. 4. It does not provide the exact location of closed-loop poles in left or right-half of s-plane Which of the above statements are correct?
The method for determination of the stability of the feedback systems as a function of an adjustable gain parameter which does not provide detailed information concerning location of closed-loop poles as a function of gain K is called
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 1. a pair of real roots with opposite sign 2. complex conjugate roots on the imaginary axis 3. a pair of complex conjugate roots with opposite real parts Which of the above statements are correct?
A system which has some roots with real parts equal to zero, but none with positive real parts, is
The input x[n] and output y[n] of a discrete-time system are related as y[n] = αy [n - 1] + x[n]. The condition on α for which the system is Bounded-Input Bounded-Output (BIBO) stable is
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 system is stable … Y: The system is unstable … Z: The test breaks down … P: … when all elements are positive Q: … when any one element is zero R: … when there is a change in sign of coefficients
Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane?
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