6. Zero in the First Column of Routh Array

When a zero occurs in the first column of Routh array, create a Routh table using the polynomial that has the reciprocal roots of the original polynomial.

e.g.: For the polynomial, \(s^5+2s^4+3s^3+6s^2+5s+3=0\), we will get the Routh table with first column to be zero.

By replacing \(s\) with \(1/s\), we get \[\frac{1}{s^5}+\frac{2}{s^4} + \frac{3}{s^3} + \frac{6}{s^2} + \frac{5}{s} + 3 = 1+2s+3s^2+6s^3+5s^4+3s^5\]

>> p = [1 2 3 6 5 3];

p =

1 2 3 6 5 3

>> roots(p)

ans =

0.3429 + 1.5083i
0.3429 - 1.5083i
-1.6681 + 0.0000i
-0.5088 + 0.7020i
-0.5088 - 0.7020i

>>