Open AccessStability of a class of neutral stochastic functional differential equations with Markovian switching
Author(s) -
Song Ruili,
Lu Boliang,
Zhu Quanxin
Publication year - 2018
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.2017.0806
Subject(s) - mathematics , exponential stability , martingale (probability theory) , lyapunov function , stochastic differential equation , stability (learning theory) , control theory (sociology) , moment (physics) , differential equation , markov process , convergence (economics) , exponential function , constant (computer programming) , mathematical analysis , computer science , nonlinear system , statistics , physics , control (management) , classical mechanics , quantum mechanics , machine learning , artificial intelligence , economics , programming language , economic growth
This study investigates the stability of a class of neutral stochastic functional differential equations with Markovian switching. Some novel stability criteria are first established, including boundedness, p th moment exponential stability and almost sure exponential stability, based on multiple Lyapunov functions, generalised Itô formula and non‐negative semi‐martingale convergence theorem. Concretely, the authors generalise the existing results under the essential neutral term and improve the diffusion operators from being controlled by two auxiliary functions to other multiple auxiliary functions with not only constant coefficients but also time‐varying coefficients. Some numerical examples are presented to illustrate the effectiveness of the obtained results.