Open AccessResults on stability of switched discrete‐time systems with all subsystems unstable
Author(s) -
Mao Xiang,
Zhu Hui,
Chen Wei,
Zhang Hongbin
Publication year - 2019
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.2018.5575
Subject(s) - dwell time , control theory (sociology) , discrete time and continuous time , mathematics , instant , lyapunov function , bounded function , divergence (linguistics) , stability (learning theory) , switching time , upper and lower bounds , computer science , control (management) , mathematical analysis , engineering , statistics , artificial intelligence , machine learning , medicine , clinical psychology , linguistics , physics , philosophy , quantum mechanics , nonlinear system , electrical engineering
In this study, the stability problem of discrete‐time switched systems without stable subsystems is considered. Using the k ‐sample‐like method, the authors construct a Lyapunov function whose value at the switching instant is less than the value at the last switching instant when the corresponding dwell time belongs to a special time span. According to whether the dwell time belongs to the time span, switchings are divided into two categories: the switching without divergence time and the switching with divergence time. Based on that, a new less conservative exponential stability theorem is established with the bounded maximum average dwell time. Furthermore, by jointly considering the dynamic characteristics of the subsystems before and after switching instants, they also give the stability result via the dwell time with the floating lower and upper bounds. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.