Open AccessExponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay
Author(s) -
Wang Hui,
Xu Huiling,
Chen Xuefeng,
Zhang Dan
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.2020.0013
Subject(s) - control theory (sociology) , linear matrix inequality , lemma (botany) , mathematics , discrete time and continuous time , reduction (mathematics) , stability (learning theory) , exponential stability , exponential function , computer science , mathematical optimization , control (management) , mathematical analysis , nonlinear system , statistics , ecology , physics , geometry , poaceae , quantum mechanics , artificial intelligence , machine learning , biology
This study tackles the problems of exponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay. The well‐posedness, exponential stability, and contractiveness of spatially interconnected discrete‐time systems subject to time‐varying delay are defined and a sufficient condition in terms of linear matrix inequality (LMI) is put forth to test these properties. By exploiting the above analysis result, a sufficient condition for guaranteeing the existence of a reduced‐order system is derived. With the help of Finsler lemma, a reduced‐order system is derived based on the LMI method. By taking advantage of the same method, a delay‐free reduced‐order system for a given spatially interconnected discrete time‐varying delay system can also be attained. Finally, two examples have been carried out to show the feasibility and validity of the derived theories.