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On aperiodicity theorems. (English) Zbl 1012.93029
This well-written paper describes a set of necessary and sufficient conditions for aperiodicity of a polynomial, i.e. conditions for the roots of a real polynomial to be real, simple, and confined to a given interval on the real axis. The conditions are (1) a positivity condition on a auxiliary polynomial along the specified real axis interval; (2) alternating sign conditions on the values taken by the polynomial and its derivatives at the bounds of the interval. Previous work on the topic is surveyed, and some applications in linear systems control theory are mentioned in the introduction.

MSC:
93C05 Linear systems in control theory
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
26C10 Real polynomials: location of zeros
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