The Routh table is a powerful analysis tool used to determine how many roots of a given polynomial have negative, zero, and positive real parts. A special case occurs when a row of zeros is encountered. This indicates an even polynomial may be factored from the given polynomial. It is well known that the even polynomial is in the row above the row of zeros. In this technical note it will be shown that the even polynomial may be factored from all of the polynomials in the rows above the row of zeros.
DorfR. C.BishopR. H.Modern control systems, tenth edition, (Prentice Hall, New Saddle River, New Jersey2005)
2.
FranklinG. F.PowellJ. D.Emami-NaeiniA.Feedback control of dynamic systems, fifth edition (Prentice Hall, New Saddle River, New Jersey)
3.
MastsumotoN.‘Simple proof of the Routh stability criterion based on order reduction of polynomials and principle of argument.’ In Proceedings of the IEEE International Symposium onCircuits and systems, Sydney, Australia. pp. 699–702 (IEEE, Piscataway, New Jersey).
