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DFCCIL Junior Executive Electrical 2018 Official Paper

Option 1 : 0 < K

__Routh-Hurwitz Stability Criterion__:

- It is used to test the stability of an LTI system.
- According to the Routh tabulation method, the system is said to be stable if there are no sign changes in the first column of the Routh array.
- The number of poles lies on the right half of s plane = number of sign changes.
- If there is a change in sign 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.

__Application__:

F(s) = 6s + K

By applying the Routh tabulation method, we get:

\(\begin{array}{*{20}{c}} {{}}{{}}{{}} {{s^1}}\\ {{s^0}} \end{array}\left| {\begin{array}{*{20}{c}} {{}{}} {6}&{0}\\ {K}&0 \end{array}} \right.\)

System stable when

**K > 0**

A row of zeros in a Routh table:

This situation occurs when the characteristic equation has

- a pair of real roots with opposite sign (±a)
- complex conjugate roots on the imaginary axis (± jω)
- a pair of complex conjugate roots with opposite real parts (-a ± jb, a ± jb)