Open AccessImproved stability and stabilisation criteria for discrete time‐delay systems via a novel double summation inequality
Author(s) -
Zhao Tao,
Liang Weibo,
Dian Songyi,
Xiao Jian,
Wei Zhenbo
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0791
Subject(s) - control theory (sociology) , stability (learning theory) , inequality , mathematics , discrete time and continuous time , computer science , control (management) , statistics , mathematical analysis , artificial intelligence , machine learning
This study focuses on the problem of stability analysis and stabilisation for discrete time‐delay systems. A new type of augmented Lyapunov–Krasovskii functional (LKF) is proposed to derive less conservative stability and stabilisation conditions. A novel inequality is developed to handle more general double summation terms which arise from the forward difference of augmented LKF. Several zero equalities are introduced to further relax the existing results. Using some advanced convexificator techniques, the derived stability and stabilisation conditions are presented in terms of linear matrix inequalities. Several numerical examples are provided to demonstrate the advantage of the proposed approach.