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On the preservation of stability in families of polynomials via substitutions
Author(s) -
FernándezAnaya Guillermo,
AlvarezRamírez José
Publication year - 2000
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 - 10.1002/1099-1239(20000715)10:8<671::aid-rnc505>3.0.co;2-x
Subject(s) - polynomial , mathematics , stability (learning theory) , representation (politics) , hadamard transform , stable polynomial , nonlinear system , kharitonov's theorem , pure mathematics , combinatorics , matrix polynomial , discrete mathematics , square free polynomial , computer science , mathematical analysis , physics , quantum mechanics , machine learning , politics , political science , law
In this work, we use the Hadamard representation of polynomials and several known results on the stability of polynomial families to describe new polynomial families which are stable under substitutions. Such polynomial families can be seen as nonlinear stable perturbations of ‘small‐in‐parameters’ polynomials. Also, the stability condition can be obtained of the positive definitness of certain Bezoutians associated with the even and odd parts of the resulting polynomial families. Some implications of our results for control analysis and design are discussed. Copyright © 2000 John Wiley & Sons, Ltd.