isHurwitzStable -- determines whether or not a rational univariate polynomial is Hurwitz stable

Synopsis

• Usage:

  isHurwitzStable(f)

• Inputs:
  • f, a ring element, a rational univariate polynomial
• Outputs:
  • a Boolean value, the Hurwitz stability of a rational univariate polynomial f

Description

Recall that a univariate polynomial is Hurwitz stable if all its roots have negative real parts. This method determines the Hurwitz stability of a rational univariate polynomial fwith positive leading coefficient and degree at least 1. The polynomial, however, is not necessarily from a univariate polynomial ring.

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing

i2 : f = 3*x^4 - 7*x^3 + 5*x - 7 

       4     3
o2 = 3x  - 7x  + 5x - 7

o2 : R

i3 : g = x^2 + 10*x + 21

      2
o3 = x  + 10x + 21

o3 : R

i4 : isHurwitzStable(f)

o4 = false

i5 : isHurwitzStable(g)	      

o5 = true

See also

• HurwitzMatrix -- a specified principle submatrix of the Hurwitz matrix of a univariate polynomial