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

被引：28
作者：
Gyurkovics, E. [1 ]
Kiss, K. [1 ]
Nagy, I. [1 ]
Takacs, T. [2 ]
机构：
[1] Budapest Univ Technol & Econ, Math Inst, Pf 91, H-1521 Budapest, Hungary
[2] Corvinus Univ Budapest, 8 Fovcint Ter, H-1093 Budapest, Hungary
来源：
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2017年 / 354卷 / 01期
基金：
匈牙利科学研究基金会;
关键词：
Delay control systems - Numerical methods - Timing circuits - System stability;
D O I：
10.1016/j.jfranklin.2016.10.006
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码：123 / 144
页数：22
相关论文
共 27 条
[1]  
[Anonymous], 2004, ORTHOGONAL POLYNOMIA, DOI DOI 10.1093/OSO/9780198506720.001.0001, Patent No. 220512815
[2]  
[Anonymous], 2014, Systems & control: foundations & applications, Introduction to time-delay systems, DOI DOI 10.1007/978-3-319-09393-2
[3]  
[Anonymous], 2009, CAUCHYS EQUATION JEN
[4]  
[Anonymous], 10 IFAC WORKSH TIM D
[5]  
Briat Corentin, 2014, LINEAR PARAMETER VAR
[6]   A note on Wirtinger-type integral inequalities for time-delay systems [J].
Gyurkovics, Eva .
AUTOMATICA, 2015, 61 :44-46
[7]   ROBUST DYNAMIC OUTPUT FEEDBACK GUARANTEED COST CONTROL FOR DISCRETE-TIME SYSTEMS WITH TIME-VARYING DELAYS [J].
Gyurkovics, Eva ;
Takacs, Tibor .
ASIAN JOURNAL OF CONTROL, 2015, 17 (02) :687-698
[8]  
Hardy G., 1952, INEQUALITIES
[9]  
Hien L.V., 2015, ARXIV150506344
[10]  
Kiss K., COMPUTATIONS DISCRET
123