Stability Criteria for Polynomials

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What is the difference between absolute and relative stability?

Absolute stability refers to whether a system is stable or unstable, while relative stability refers to the degree of stability. (correct)
Absolute stability is used for BIBO stability, while relative stability is used for impulse response.
Absolute stability refers to the degree of stability, while relative stability refers to whether a system is stable or unstable.
Absolute stability is used for impulse response, while relative stability is used for BIBO stability.

What is the necessary and sufficient condition for a feedback system to be stable?

All poles of the system transfer function have imaginary real parts.
All poles of the system transfer function have negative real parts. (correct)
All poles of the system transfer function have zero real parts.
All poles of the system transfer function have positive real parts.

What is the effect of pole locations on the unit step response of a 2nd-order system?

The system is unstable if all poles have zero real parts.
The system is stable if all poles have negative real parts. (correct)
The system is stable if all poles have positive real parts.
The system is unstable if all poles have negative real parts.

What is the condition for a system to be BIBO stable?

The system has a bounded response to a bounded input. (A) Signup and view all the answers

What is the form of the poles of the standard transfer function of a 2nd-order system?

s1, 2 = -ζωn ± j1 - ζ2 (A) Signup and view all the answers

Is the system G(s) = 10(s+2)/(s+1)(s-3)(s+4) stable?

No, the system is unstable. (B) Signup and view all the answers

What is the Routh array used for?

To determine the stability of a system (C) Signup and view all the answers

What is the form of the response transform X1(s)?

X1(s) = bn s^n + bn-1 s^n-1 +... + b1s + b0 (C) Signup and view all the answers

What is the characteristic equation of the system?

Q(s) = bn s^n + bn-1 s^n-1 +... + b1s + b0 = 0 (A) Signup and view all the answers

How are the constants c1, c2, c3, etc. evaluated in the Routh array?

By using the coefficients of the characteristic equation (A) Signup and view all the answers

What is the condition for stability of a system according to Routh's criterion?

All terms in the first column have the same sign (C) Signup and view all the answers

What is the number of roots of the characteristic equation with positive real parts equal to?

The number of changes of sign of the coefficients in the first column (C) Signup and view all the answers

What does the presence of imaginary roots in the characteristic equation indicate about the output of the system?

The output includes a sinusoidally oscillating component (A) Signup and view all the answers

What is the next step after finding the characteristic equation of a system?

Form the auxiliary equation from the preceding row (D) Signup and view all the answers

What is the condition for a system to be stable according to the Routhian array method?

There are no changes of sign in the first column (D) Signup and view all the answers

What is the purpose of differentiating the auxiliary equation in the Routhian array method?

To complete the Routhian array (A) Signup and view all the answers

What is the condition for the numerator of the first term in the s1 row to be positive for a stable system?

–K2 – 43K + 2000 > 0 (D) Signup and view all the answers

What is the range of K for which the system is stable in the given example?

K < 80 and K > 0 (B) Signup and view all the answers

What is the necessary condition for a stable system?

All the coefficients of the characteristic equation have the same sign (A) Signup and view all the answers

What is the Routh-Hurwitz stability criterion used for?

To determine the number of roots of q(s) with positive real parts (A) Signup and view all the answers

What is the first step in the Routh-Hurwitz stability test?

To construct the Routh array from the system characteristic equation (A) Signup and view all the answers

What is the characteristic equation of a system?

The equation q(s) = 0 (C) Signup and view all the answers

What is the purpose of the Routh-Hurwitz stability test?

To determine the stability of a SISO-LTI system (A) Signup and view all the answers

What is the necessary and sufficient condition for a stable system?

The Routh-Hurwitz test is satisfied (A) Signup and view all the answers

What is the condition for all roots of the 1st Order polynomial Q(s) = a1s + a0 to be in the Left Half Plane (LHP)?

a1 and a0 have the same sign (A) Signup and view all the answers

What is the condition for all roots of the 2nd Order polynomial Q(s) = a2s^2 + a1s + a0 to be in the LHP?

a2, a1, and a0 have the same sign (C) Signup and view all the answers

What is the condition for all roots of the Higher Order polynomial Q(s) = an s^n + an-1s^n-1 +... + a1s + a0 to be in the LHP?

All coefficients ak have the same sign (D) Signup and view all the answers

What is the limitation of the Routh-Hurwitz criterion?

It is only applicable to polynomials (D) Signup and view all the answers

What is the value of K for which the system is stable in the given example?

0 < K < 28.1 (C) Signup and view all the answers