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Special cases of Routh’s criteria |
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Answer» Case 1: All the elements of a row in a RA are zero • Form Auxiliary equation by using the co-efficient of the row which is just above the row of zeros • Find derivative of the A.E. • Replace the row of zeros by the co-efficient of dA(s)/ds • complete the array in terms of these coefficients • analyze for any sign change, if so, unstable • no sign change, find the nature of roots of AE • non-repeated imaginary roots - marginally stable • repeated imaginary roots – unstable Case 2: First element of any of the rows of RA is • Zero and the same remaining row contains at least one non-zero element • Substitute a small positive no. “ε‘ in place of zero and complete the array. • Examine the sign change by taking Lt ε = 0 |
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