Kharitonov region

A Kharitonov region is a concept in mathematics. It arises in the study of the stability of polynomials.

Let ${\displaystyle D}$ be a simply-connected set in the complex plane and let ${\displaystyle P}$ be the polynomial family.

${\displaystyle D}$ is said to be a Kharitonov region if

${\displaystyle V_{T}^{n}(V_{S}^{n})}$

is a subset of ${\displaystyle P.}$ Here, ${\displaystyle V_{T}^{n}}$ denotes the set of all vertex polynomials of complex interval polynomials ${\displaystyle (T^{n})}$ and ${\displaystyle V_{S}^{n}}$ denotes the set of all vertex polynomials of real interval polynomials ${\displaystyle (S^{n}).}$