aa
Section 5–6 / Routh’s Stability Criterion 213
3.If all coefficients are positive, arrange the coefficients of the polynomial in rows
and columns according to the following pattern:
The process of forming rows continues until we run out of elements. (The total number
of rows is n+1.) The coefficients b 1 ,b 2 ,b 3 , and so on, are evaluated as follows:
The evaluation of the b’s is continued until the remaining ones are all zero. The same
pattern of cross-multiplying the coefficients of the two previous rows is followed in
evaluating the c’s,d’s,e’s, and so on. That is,
c 3 =
b 1 a 7 - a 1 b 4
b 1
c 2 =
b 1 a 5 - a 1 b 3
b 1
c 1 =
b 1 a 3 - a 1 b 2
b 1
b 3 =
a 1 a 6 - a 0 a 7
a 1
b 2 =
a 1 a 4 - a 0 a 5
a 1
b 1 =
a 1 a 2 - a 0 a 3
a 1
sn
sn-^1
sn-^2
sn-^3
sn-^4
s^2
s^1
s^0
a 0
a 1
b 1
c 1
d 1
e 1
f 1
g 1
a 2
a 3
b 2
c 2
d 2
e 2
a 4
a 5
b 3
c 3
d 3
a 6
a 7
b 4
c 4
d 4
p
p
p
p
p
