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A weak kharitonov theorem holds if and only if the stability region and its reciprocal are convex
Author(s) -
Rantzer Anders
Publication year - 1993
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590030104
Subject(s) - kharitonov's theorem , mathematics , stability (learning theory) , reciprocal , regular polygon , class (philosophy) , pure mathematics , interval (graph theory) , convex combination , discrete mathematics , combinatorics , mathematical analysis , convex optimization , polynomial , computer science , geometry , linguistics , philosophy , matrix polynomial , machine learning , artificial intelligence , square free polynomial
We give necessary and sufficient conditions on the stability region for the validity of a weak version of Kharitonov's theorem, stating that stability of an ‘interval family’ of complex polynomials is implied by stability of the corner polynomials. Furthermore, we define a class of stability regions which do not satisfy the conditions, but for which the implication still holds in the case of real polynomials.