Kharitonov region

A Kharitonov region is a concept in mathematics. It arises in the study of the stability of polynomials. Let [math]\displaystyle{ D }[/math] be a simply-connected set in the complex plane and let [math]\displaystyle{ P }[/math] be the polynomial family.

[math]\displaystyle{ D }[/math] is said to be a Kharitonov region if

[math]\displaystyle{ V_T^n(V_S^n) }[/math]

is a subset of [math]\displaystyle{ P. }[/math] Here, [math]\displaystyle{ V_T^n }[/math] denotes the set of all vertex polynomials of complex interval polynomials [math]\displaystyle{ (T^n) }[/math] and [math]\displaystyle{ V_S^n }[/math] denotes the set of all vertex polynomials of real interval polynomials [math]\displaystyle{ (S^n). }[/math]

See also

• Kharitonov's theorem

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.