Multiple summation inequalities and their application to stability analysis of discrete-time delay systems

This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen׳s and Wirtinger׳s inequalities, as well as the recently presented inequalities for sin...

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Veröffentlicht in:	Journal of the Franklin Institute 2017-01, Vol.354 (1), p.123-144
Hauptverfasser:	Gyurkovics, É., Kiss, K., Nagy, I., Takács, T.
Format:	Artikel
Sprache:	eng
Schlagworte:	Convex analysis Delay time analysis Discrete time systems Functionals Inequalities Numerical methods Polynomials Stability analysis Time delay systems
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creator	Gyurkovics, É. Kiss, K. Nagy, I. Takács, T.
description	This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen׳s and Wirtinger׳s inequalities, as well as the recently presented inequalities for single and double summation in [16]. The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for the comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.
doi_str_mv	10.1016/j.jfranklin.2016.10.006
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subjects	Convex analysis Delay time analysis Discrete time systems Functionals Inequalities Numerical methods Polynomials Stability analysis Time delay systems
title	Multiple summation inequalities and their application to stability analysis of discrete-time delay systems
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