Open AccessStability and ℓ ∞ ‐gain analysis for discrete‐time positive singular systems with unbounded time‐varying delays
Author(s) -
Huong Dinh Cong,
Sau Nguyen Huu
Publication year - 2020
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.2019.0933
Subject(s) - control theory (sociology) , monotonic function , discrete time and continuous time , stability (learning theory) , trajectory , mathematics , state (computer science) , exponential stability , small gain theorem , computer science , mathematical analysis , control (management) , nonlinear system , algorithm , physics , statistics , astronomy , artificial intelligence , machine learning , quantum mechanics
This study considers the stability and ℓ ∞ ‐gain analysis problem for discrete‐time positive singular systems with unbounded time‐varying delays. By proposing some new techniques and employing mathematical induction method, the authors first derive a sufficient condition to analyse the stability of the system. The authors then investigate the ℓ ∞ ‐gain by exploiting the monotonicity of state trajectory. They show that the ℓ ∞ ‐gain for the considered systems is independent of the magnitude of delays and fully determined by the system matrices. The validity of the theoretical results is demonstrated by a numerical example.