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Polynomials‐based summation inequalities and their applications to discrete‐time systems with time‐varying delays
Author(s) -
Lee Seok Young,
Lee Won Il,
Park PooGyeon
Publication year - 2017
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.3755
Subject(s) - mathematics , polynomial , inequality , summation by parts , discrete time and continuous time , function (biology) , order (exchange) , log sum inequality , stability (learning theory) , pure mathematics , algebra over a field , mathematical analysis , computer science , statistics , finance , evolutionary biology , machine learning , economics , biology
Summary This paper proposes a novel summation inequality, say a polynomials‐based summation inequality, which contains well‐known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete‐time counterpart of Wirtinger‐based integral inequality, auxiliary function‐based summation inequalities employing the same‐order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials‐based summation inequality employing first‐order and second‐order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete‐time systems with time‐varying delays. Copyright © 2017 John Wiley & Sons, Ltd.