Open AccessQuasi‐convex combination method and its application to the stability analysis of 2D discrete‐time Roesser systems with time‐varying delays
Author(s) -
Huang Yi Bo,
An Jianqi,
He Yong,
Wu Min
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.2017.0653
Subject(s) - discrete time and continuous time , linear matrix inequality , mathematics , control theory (sociology) , stability (learning theory) , regular polygon , convex combination , stability criterion , convex optimization , lyapunov function , mathematical optimization , circle criterion , computer science , exponential stability , nonlinear system , control (management) , statistics , geometry , artificial intelligence , machine learning , physics , quantum mechanics
This study is concerned with the problem of stability analysis of two‐dimensional (2D) discrete‐time Roesser systems with time‐varying delays. First, based on an augmented Lyapunov–Krosovskii functional, a less conservative stability criterion incorporating time‐varying terms is established by utilising a general free‐matrix‐based inequality. Next, in order to eliminate the time‐varying terms without introducing redundant constraints, a quasi‐convex combination method is proposed. Then, compared with the criteria derived via the other inequalities, the conservatism analysis is given to prove the proposed criterion can lead to a better result theoretically. Finally, a numerical example is presented to illustrate the advantage of the presented method.