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Boundary testing of stability for the family of nonlinear parametrized real polynomials
Author(s) -
Wang EnPing,
Geng ZhiYong
Publication year - 1997
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/(sici)1099-1239(199711)7:11<989::aid-rnc247>3.0.co;2-m
Subject(s) - mathematics , boundary (topology) , stability (learning theory) , nonlinear system , domain (mathematical analysis) , boundary value problem , class (philosophy) , difference polynomials , space (punctuation) , parameter space , mathematical analysis , orthogonal polynomials , pure mathematics , computer science , geometry , physics , quantum mechanics , machine learning , artificial intelligence , operating system
This paper studies the robust stability of the polynomials which are parametrized in a nonlinear way by the establishment of the concept of single‐directed conditional extreme value. The necessary and sufficient condition to determine the stability of the family of polynomials by testing the boundary of the parameter domain is presented for the situation when the mapping from parameter space to the coefficient space is continuous. Therefore the method of boundary testing used for checking the stability of linearly parametrized polynomials is generalized to a class of polynomials which satisfies the conditions given in this paper. © 1997 by John Wiley & Sons, Ltd.