Open AccessStability of switched singular time delay systems with switching induced state jumps
Author(s) -
Lin Jinxing,
Wu Xiang,
Ding Jie,
Lou ZhiE
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.2019.1338
Subject(s) - dwell time , control theory (sociology) , upper and lower bounds , mathematics , interval (graph theory) , state (computer science) , exponential stability , function (biology) , jump , stability (learning theory) , lyapunov function , state dependent , switching time , computer science , mathematical analysis , algorithm , physics , control (management) , artificial intelligence , machine learning , medicine , clinical psychology , mathematical economics , optoelectronics , combinatorics , nonlinear system , quantum mechanics , evolutionary biology , biology
This study addresses the problem of exponential stability for switched singular state‐delayed systems with switching induced state jumps, which has not been studied up to now. The considered state delay varies in a time‐varying interval. On the basis of equivalent dynamics decomposition, a model of state jump at switching instants is firstly established under an assumption that the time length between arbitrary two adjacent switches is larger than the upper bound of the state delay. Then, a sufficient condition on exponential stability of the system under the reranged dwell‐time switching constraint is presented. The key idea is the design of a dwell‐time‐dependent generalised Lyapunov function as well as a dwell‐time‐dependent function with respect to algebraic variables and application of the Razumikhin approach. The obtained stability condition exploits the lower bound and the upper bound of the dwell time. In addition, it is independent of the size of the state delay and allows the delay to be a fast time‐varying function. Finally, two numerical examples are given to show the efficacy of the derived result.