A complex polynomial is called a Hurwitz polynomial, if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical (analog or digital) networks. In this article we prove that a polynomial p can be shown to be Hurwitz by checking whether the rational function e(p)/o(p) can be realized as a reactance one port, that is as ...

In the current paper, the finite-sample stability of various implementations of the KPSS test is studied. The implementations considered differ in how the so-called long-run variance is estimated under the null hypothesis. More specifically, the effects that the choice of kernel, the value of the bandwidth parameter and the application of a prewhitening filter have on the KPSS test are investig...

Owing to several uncertainties in the modelling of a system, checking for “robust stability” is, in fact, a more practical goal for any designer. In this, instead of a single matrix A, a family of matrices (A + δA) has to be checked for negative definiteness. This led us to the question “How long does a computer take to check the sign definiteness of a family of matrices?” Mathematically, we st...

The words of a language are randomly replaced in time by new ones, but long since it was observed that words corresponding to some items (meanings) are less frequently replaced then others. Usually, the rate of replacement for a given item is not directly observable, but it is inferred by the estimated stability which, on the contrary, is observable. This idea goes back a long way in the lexico...