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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?

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? Correct Answer 1, 2 and 4 only

Routh- Hurwitz Criterion:

Routh Hurwitz criterion states that any system can be stable if and only if all the roots of the first column have the same sign and if it does not has the same sign or there is a sign change then the number of sign changes in the first column is equal to the number of roots of the characteristic equation in the right half of the s-plane i.e. equals to the number of roots with positive real parts.

 

Advantages:

  • We can find the stability of the system without solving the equation.
  • We can easily determine the relative stability of the system.
  • We can determine the range of K for stability.
  • We can also determine the point of intersection for root locus with an imaginary axis.

 

Limitations:

  • This criterion is applicable only for a linear system.
  • It does not provide the exact location of poles on the right and left half of the S plane.
  • In case of the characteristic equation, it is valid only for real coefficients.

Related Questions

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2. The complex Fourier series coefficients of x(3f) are {3ak} where k is integer valued.
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4. Phenomena have no essence, but only nature.