A Kharitonov region is a concept in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

. It arises in the study of the stability of polynomials. Let

D

be a

simply-connected set In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the spac ...

in the

complex plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...

and let

P

be the polynomial family.

D

is said to be a Kharitonov region if :

V_T^n(V_S^n)

is a subset of

P.

Here,

V_T^n

denotes the set of all

vertex polynomial Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

s of complex interval polynomials

(T^n)

and

V_S^n

denotes the set of all vertex polynomials of real interval polynomials

(S^n).

References

* Y C Soh and Y K Foo (1991), “Kharitonov Regions: It Suffices to Check a Subset of Vertex Polynomials”, IEEE Trans. on Aut. Cont., 36, 1102 – 1105. Polynomials Stability theory {{algebra-stub

See also

References