Open AccessStabilisation of coupled delayed regime‐switching diffusion with continuous‐state‐dependent switching via intermittent control
Author(s) -
Xu Yao,
Chu Chenyin,
Li Wenxue
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.2018.6335
Subject(s) - control theory (sociology) , diffusion , coupling (piping) , moment (physics) , controller (irrigation) , process (computing) , stability (learning theory) , diffusion process , work (physics) , mathematics , computer science , control (management) , physics , engineering , artificial intelligence , thermodynamics , mechanical engineering , agronomy , knowledge management , innovation diffusion , classical mechanics , machine learning , biology , operating system
Motivated by Markovian regime‐switching diffusion (MRSD), time‐varying delays and non‐linear coupling forms, this study is concerned with stabilisation of coupled regime‐switching diffusion with time‐varying delays (CRSDTD) under periodically intermittent control. Compared with most papers investigating MRSD, a striking feature of regime‐switching diffusion is that in the two‐component process ( x ( t ) , α ( t ) ) , switching process α ( t ) depends on the diffusion x ( t ) , which can be regarded as the x ‐dependent process briefly. It is worth mentioning that time‐varying delays and non‐linear coupling forms are taken into consideration when modelling, which makes their work more realistic. Moreover, a periodically intermittent controller is adopted to guarantee that CRSDTD can achieve the p th moment exponential stability and some sufficient conditions are derived by using the Lyapunov method and Kirchhoff's matrix tree theorem. Furthermore, to illustrate the applicability of their theoretical results, an application to regime‐switching coupled oscillators with time‐varying delays (RSCOTD) is presented and a stability criterion is given. Conclusively, numerical simulations on RSCOTD are presented to illustrate the effectiveness of the theoretical results.