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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Franklin Institute 2017-01, Vol.354 (1), p.123-144
Main Authors: Gyurkovics, É., Kiss, K., Nagy, I., Takács, T.
Format: Article
Language:English
Subjects:
Convex analysis
Delay time analysis
Discrete time systems
Functionals
Inequalities
Numerical methods
Polynomials
Stability analysis
Time delay systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2016.10.006