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{{Orphan|date=February 2013}} | |||
{{Expert-subject|Mathematics|date=February 2009}} | |||
A '''Kharitonov region''' is a concept in [[mathematics]]. It arises in the study of the [[Stable polynomial|stability of polynomials]]. | |||
Let <math>D</math> be a [[simply-connected set]] in the [[complex plane]] and let <math>P</math> be the polynomial family. | |||
<math>D</math> is said to be a '''Kharitonov region''' if | |||
:<math>V_T^n(V_S^n)</math> | |||
is a subset of <math>P.</math> Here, <math>V_T^n</math> denotes the set of all [[vertex polynomial]]s of complex interval polynomials <math>(T^n)</math> and <math>V_S^n</math> denotes the set of all vertex polynomials of real interval polynomials <math>(S^n).</math> | |||
==See also== | |||
*[[Kharitonov's theorem]] | |||
==References== | |||
{{reflist}} | |||
* 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. | |||
[[Category:Polynomials]] | |||
{{algebra-stub}} | |||
Revision as of 23:33, 30 January 2014
Template:Expert-subject A Kharitonov region is a concept in mathematics. It arises in the study of the stability of polynomials.
Let be a simply-connected set in the complex plane and let be the polynomial family.
is said to be a Kharitonov region if
is a subset of Here, denotes the set of all vertex polynomials of complex interval polynomials and denotes the set of all vertex polynomials of real interval polynomials
See also
References
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- 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.