Open AccessDelay‐dependent stability of non‐linear hybrid stochastic functional differential equations
Author(s) -
Song Ruili,
Wang Bo,
Zhu Quanxin
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.2019.0329
Subject(s) - mathematics , exponential stability , stability (learning theory) , lyapunov function , control theory (sociology) , stochastic differential equation , differential equation , class (philosophy) , stability theory , delay differential equation , differential (mechanical device) , nonlinear system , mathematical analysis , computer science , control (management) , physics , quantum mechanics , machine learning , artificial intelligence , aerospace engineering , engineering
This study investigates delay‐dependent stability of a class of highly non‐linear stochastic functional differential equations with Markovian switching. Some novel boundedness and stability criteria are first established, including H ∞stability in L p , asymptotic stability in L p and almost surely asymptotic stability, based on Lyapunov functions and generalised Itô formula. Concretely, the authors generalise and improve the existing results to the hybrid stochastic functional differential equations case. An example is presented to illustrate the effectiveness of the obtained results.