Open AccessStability of two‐dimensional Roesser systems with time‐varying delays via novel 2D finite‐sum inequalities
Author(s) -
Van Hien Le,
Trinh Hieu
Publication year - 2016
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.2016.0078
Subject(s) - mathematics , control theory (sociology) , stability (learning theory) , interval (graph theory) , linear matrix inequality , discrete time and continuous time , range (aeronautics) , upper and lower bounds , inequality , jensen's inequality , matrix (chemical analysis) , mathematical optimization , mathematical analysis , computer science , convex optimization , control (management) , engineering , statistics , regular polygon , materials science , combinatorics , machine learning , artificial intelligence , composite material , aerospace engineering , geometry , convex analysis
This study considers the problem of stability analysis of discrete‐time two‐dimensional (2D) Roesser systems with interval time‐varying delays. New 2D finite‐sum inequalities, which provide a tighter lower bound than the existing ones based on 2D Jensen‐type inequalities, are first developed. Based on an improved Lyapunov–Krasovskii functional, the newly derived inequalities are then utilised to establish delay‐range‐dependent linear matrix inequality‐based stability conditions for a class of discrete time‐delay 2D systems. The effectiveness of the obtained results is demonstrated by numerical examples.