Open AccessStabilisation of highly non‐linear continuous‐time hybrid stochastic differential delay equations by discrete‐time feedback control
Author(s) -
Mei Chunhui,
Fei Chen,
Fei Weiyin,
Mao Xuerong
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.2019.0822
Subject(s) - control theory (sociology) , discrete time and continuous time , mathematics , stochastic differential equation , delay differential equation , stability theory , lyapunov function , differential equation , controller (irrigation) , upper and lower bounds , linear differential equation , computer science , nonlinear system , control (management) , mathematical analysis , physics , statistics , artificial intelligence , quantum mechanics , agronomy , biology
In this study, the authors consider how to use discrete‐time state feedback to stabilise hybrid stochastic differential delay equations. The coefficients of these stochastic differential delay equations do not satisfy the conventional linear growth conditions, but are highly non‐linear. Using the Lyapunov functional method, they show that a discrete feedback controller, which depends on the states of the discrete‐time observations, can be designed to make the solutions of such controlled hybrid stochastic differential delay equations asymptotically stable and exponentially stable. The upper bound of the discrete observation interval τ is also given in this study. Finally, a numerical example is given to illustrate the proposed theory.