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Stability of Polynomials and the Hurwitz Criterion.

It often occurs that people are uninterested in the exact numerical values of the roots of the polynomial in question. Instead, they wish to know whether or not its roots are all in the left half plane, in which case the polynomial is said to be stable. Such applications occur in control theory, for example.

It is not as well-known as it should be that this question can be decided without reference to the numerical value of the roots, and indeed even if the coefficients depend on a parameter one can put useful conditions on the parameter that guarantee stability of the polynomial in question.

Robert Corless
Wed Feb 28 18:25:56 EST 1996